C₄×#20263479 #38760358

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

Aliases

direct product

C₄×#20263479

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	#20263479
commutator, hypocenter	C₇²×C₄₃	C₃×C₄
Frattini	C₂	C₂×#20263479
Fitting	C₄×C₇²×C₄₃	C₃
socle, cosocle	C₂×C₇²×C₄₃	C₂×C₃
prime radical	C₂×#20263479	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)(19,28,37)(22,30,35)(25,33,32)(27,36,29)(31,40,44)(34,41,43)(38,45,39)(42,46,47)(49,50,51)(52,54,53)(56,57,58)(59,61,60);(5,6,8,12,19,24,9,13,20,29,39,36,16,23,32,28,38,45,26,35,43,40,18,27,37,44,47,46,30,11,17,25,34,42,41,21,7,10,15,22,31,33,14)(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, 165);

C4×#20263479 #38760358