#38760419

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

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₇²×C₄₃ ⋊ C₃×C₄
Hall	C₄₃⋊#5997 ⋊ C₃
Hall	#20263479 ⋊ C₄
Sylow	C₇² ⋊ (C₄₃⋊C₃)⋊C₄
Sylow	C₄₃ ⋊ #5997⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₄₃	C₃×C₄
prime radical	#27162406	C₂
cosocle	C₄₃×C₇⋊D₇	C₂×C₃
LCS	G ▷ C₇²×C₄₃
UCS	C₁

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 57
transitive degree	μ_t(G) = 602

A minimal faithful permutation representation — 2 generators on 57 points:

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

Polycyclic presentation:

2,3,2,7^2,43|a^2=c,d^a=d^4e^3,e^a=d^6e^3,f^a=f^42,d^b=d^2,e^b=e^2,f^b=f^36,d^c=d^6,e^c=e^6

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 226);