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C2×D8481 #46800192

order33924
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD16962
direct productC2×D8481
unambiguous semidirect product(C2×C3)⋊D2827
unambiguous semidirect product(C2×C11)⋊D771
unambiguous semidirect product(C2×C257)⋊D33

Splittings

Fitting, socleC2×C3×C11×C257 ⋊ C2
derived, HallC3×C11×C257 ⋊ C22
HallC11×C257 ⋊ C2×D3
HallC3×C257 ⋊ C2×D11
SylowC257 ⋊ C2×D33
HallC3×C11 ⋊ C2×D257
SylowC11 ⋊ C2×D771
SylowC3 ⋊ C2×D2827

Subgroups

subgroupG/H
center, hypercenterC2D8481
commutator, cosocle, hypocenterC3×C11×C257C22
FrattiniC1G
Fitting, socleC2×C3×C11×C257C2
LCSG ▷ C3×C11×C257
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 273
transitive degreeμt(G) = 16962

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

Conjugacy classes & character table

8484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33924, 28);