C₁₃×C₂₃×C₂²⋊ΓL(1,𝔽₈) #38737448

order	25116
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₃×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×C₂₃×C₂²⋊ΓL(1,𝔽₈)
unambiguous semidirect product	C₂²⋊(C₁₃×ΓL(1,𝔽₈)×C₂₃)
unambiguous semidirect product	C₇⋊(A₄×C₁₃×C₂₃)
unambiguous semidirect product	(C₂²×C₂₃)⋊(C₁₃×ΓL(1,𝔽₈))
unambiguous semidirect product	(C₇×C₂₃)⋊(A₄×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₃×C₂₃	C₂²⋊ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₂²×C₇	C₃×C₁₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₂²×C₇×C₁₃×C₂₃	C₃
LCS	G ▷ C₂²×C₇
UCS	C₁ ◁ C₁₃×C₂₃

40 conjugacy classes of subgroups.

μ_t(G) = 8372

3588 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 167);