C₅×C₁₃×C₁₇×ΓL(1,𝔽₈) #37550940

order	23205
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₁₃×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₃×C₁₇×ΓL(1,𝔽₈)
unambiguous semidirect product	C₇⋊(C₃×C₅×C₁₃×C₁₇)
unambiguous semidirect product	(C₅×C₇)⋊(C₃×C₁₃×C₁₇)
unambiguous semidirect product	(C₇×C₁₇)⋊(C₃×C₅×C₁₃)
unambiguous semidirect product	(C₅×C₇×C₁₇)⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₃×C₁₇	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃×C₅×C₁₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₁₇	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₁₃×C₁₇

32 conjugacy classes of subgroups.

μ_t(G) = 7735

5525 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23205, 3);