#38760324

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	C₇×Dic₇×C₄₃ ⋊ C₃
Hall	#20263480 ⋊ C₄
Hall	C₇×Dic₇ ⋊ C₄₃⋊C₃
Sylow	C₇² ⋊ C₄×C₄₃⋊C₃
Sylow	C₄₃ ⋊ #10596873

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	#27162417
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

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1204

A minimal faithful permutation representation — 2 generators on 61 points:

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

Polycyclic presentation:

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

Conjugacy classes & character table

1014 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 131);