C₄×#20263480 #38760359

order	25284
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₄×#20263480

Splittings

Fitting, Hall	C₄×C₇²×C₄₃ ⋊ C₃
derived, Hall	C₇²×C₄₃ ⋊ C₃×C₄
Hall	C₄×C₇² ⋊ C₄₃⋊C₃
Hall	C₄×C₄₃ ⋊ #3861
Sylow	C₇² ⋊ C₄×C₄₃⋊C₃
Sylow	C₄₃ ⋊ C₄×#3861

Subgroups

	subgroup	G/H
center, hypercenter	C₄	#20263480
commutator, hypocenter	C₇²×C₄₃	C₃×C₄
Frattini	C₂	C₂×#20263480
Fitting	C₄×C₇²×C₄₃	C₃
socle, cosocle	C₂×C₇²×C₄₃	C₂×C₃
prime radical	C₂×#20263480	C₂
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₄

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 8428

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4)(6,7,9)(8,11,16)(10,14,13)(12,18,26)(15,21,23)(17,24,20)(19,28,34)(22,30,35)(25,33,32)(27,36,29)(31,40,42)(37,43,41)(38,44,39)(45,47,46)(49,50,51)(52,54,53)(56,57,58)(59,61,60);(5,6,8,12,19,21,7,10,15,22,31,30,11,17,25,34,42,40,18,27,37,44,26,35,28,38,45,47,36,16,23,32,41,46,43,24,9,13,20,29,39,33,14)(55,56,57,59,58,60,61);(48,49,50,52,51,53,54)

Conjugacy classes & character table

2820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 166);

C4×#20263480 #38760359