C₂₃×D₁₃×AGL(1,𝔽₇) #38737353

order	25116
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₃×D₁₃×AGL(1,𝔽₇)
unambiguous semidirect product	D₇⋊(C₃×C₂₃×D₁₃)
unambiguous semidirect product	(ΓL(1,𝔽₈)×D₁₃)⋊(C₂×C₂₃)
unambiguous semidirect product	(C₁₃×AGL(1,𝔽₇))⋊(C₂×C₂₃)
unambiguous semidirect product	(ΓL(1,𝔽₈)⋊D₁₃)⋊(C₂×C₂₃)

	subgroup	G/H
center, hypercenter	C₂₃	D₁₃×AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₇×C₁₃	C₂²×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₂₃	C₂²×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂₃

80 conjugacy classes of subgroups.

μ_t(G) = 2093

1288 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 72);