#38760339

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

Aliases

No aliases for this group.

Splittings

derived, Hall	C₇²×C₄₃ ⋊ C₃×C₄
Hall	C₇²×Dic₄₃ ⋊ C₃
Hall	#20263480 ⋊ C₄
Hall	Dic₄₃ ⋊ #3861
Sylow	C₇² ⋊ (C₄₃⋊C₃)⋊C₄
Sylow	C₄₃ ⋊ C₄×#3861

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	#27162432
commutator, hypocenter	C₇²×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₇²×C₄₃	C₂×C₃
prime radical	C₂×#20263480	C₂
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₂

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:

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

Polycyclic presentation:

2,3,7^2,43,2|a^2=f,e^a=e^42,c^b=c^2,d^b=d^2,e^b=e^6

Conjugacy classes & character table

762 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 146);