Finite Group Databasebeta

← Prev (#36348335) Next (#36348337) →

C2×D5523 #36348336

order22092
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11046
direct productC2×D5523
unambiguous semidirect product(C2×C3)⋊D1841
unambiguous semidirect product(C2×C7)⋊D789
unambiguous semidirect product(C2×C263)⋊D21

Splittings

Fitting, socleC2×C3×C7×C263 ⋊ C2
derived, HallC3×C7×C263 ⋊ C22
HallC7×C263 ⋊ C2×D3
HallC3×C263 ⋊ C2×D7
SylowC263 ⋊ C2×D21
HallC3×C7 ⋊ C2×D263
SylowC7 ⋊ C2×D789
SylowC3 ⋊ C2×D1841

Subgroups

subgroupG/H
center, hypercenterC2D5523
commutator, cosocle, hypocenterC3×C7×C263C22
FrattiniC1G
Fitting, socleC2×C3×C7×C263C2
LCSG ▷ C3×C7×C263
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 275
transitive degreeμt(G) = 11046

A minimal faithful permutation representation — 2 generators on 275 points:

(1,2)(3,4,5)(6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275);(4,5)(7,12)(8,11)(9,10)(14,275)(15,274)(16,273)(17,272)(18,271)(19,270)(20,269)(21,268)(22,267)(23,266)(24,265)(25,264)(26,263)(27,262)(28,261)(29,260)(30,259)(31,258)(32,257)(33,256)(34,255)(35,254)(36,253)(37,252)(38,251)(39,250)(40,249)(41,248)(42,247)(43,246)(44,245)(45,244)(46,243)(47,242)(48,241)(49,240)(50,239)(51,238)(52,237)(53,236)(54,235)(55,234)(56,233)(57,232)(58,231)(59,230)(60,229)(61,228)(62,227)(63,226)(64,225)(65,224)(66,223)(67,222)(68,221)(69,220)(70,219)(71,218)(72,217)(73,216)(74,215)(75,214)(76,213)(77,212)(78,211)(79,210)(80,209)(81,208)(82,207)(83,206)(84,205)(85,204)(86,203)(87,202)(88,201)(89,200)(90,199)(91,198)(92,197)(93,196)(94,195)(95,194)(96,193)(97,192)(98,191)(99,190)(100,189)(101,188)(102,187)(103,186)(104,185)(105,184)(106,183)(107,182)(108,181)(109,180)(110,179)(111,178)(112,177)(113,176)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,169)(121,168)(122,167)(123,166)(124,165)(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)(142,147)(143,146)(144,145)

Conjugacy classes & character table

5526 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD22092
maximal normal subgroup ofD22092
maximal quotient ofDic11046, D22092

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22092, 34);