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C2×D7491 #44471985

order29964
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD14982
direct productC2×D7491
unambiguous semidirect product(C2×C3)⋊D2497
unambiguous semidirect product(C2×C11)⋊D681
unambiguous semidirect product(C2×C227)⋊D33

Splittings

Fitting, socleC2×C3×C11×C227 ⋊ C2
derived, HallC3×C11×C227 ⋊ C22
HallC11×C227 ⋊ C2×D3
HallC3×C227 ⋊ C2×D11
SylowC227 ⋊ C2×D33
HallC3×C11 ⋊ C2×D227
SylowC11 ⋊ C2×D681
SylowC3 ⋊ C2×D2497

Subgroups

subgroupG/H
center, hypercenterC2D7491
commutator, cosocle, hypocenterC3×C11×C227C22
FrattiniC1G
Fitting, socleC2×C3×C11×C227C2
LCSG ▷ C3×C11×C227
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 243
transitive degreeμt(G) = 14982

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

Conjugacy classes & character table

7494 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD29964
maximal normal subgroup ofD29964
maximal quotient ofDic14982, D29964

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29964, 24);