C₃×C₇×ΓL(1,𝔽₈)×C₅₃ #37552616

order	23373
automorphism	?
homology	Abelianization (H₁) = C₃²×C₇×C₅₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₇×ΓL(1,𝔽₈)×C₅₃
unambiguous semidirect product	C₇⋊(C₃²×C₇×C₅₃)
unambiguous semidirect product	(C₃×C₇)⋊(C₃×C₇×C₅₃)
unambiguous semidirect product	(C₇×C₅₃)⋊(C₃²×C₇)
unambiguous semidirect product	(C₃×C₇×C₅₃)⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₃×C₇×C₅₃	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃²×C₇×C₅₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₅₃	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₇×C₅₃

56 conjugacy classes of subgroups.

μ_t(G) = 3339

5565 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23373, 11);