C₃×C₁₃×ΓL(1,𝔽₈)×C₂₉ #37557655

order	23751
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₃×C₂₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₁₃×ΓL(1,𝔽₈)×C₂₉
unambiguous semidirect product	C₇⋊(C₃²×C₁₃×C₂₉)
unambiguous semidirect product	(C₃×C₇)⋊(C₃×C₁₃×C₂₉)
unambiguous semidirect product	(C₇×C₂₉)⋊(C₃²×C₁₃)
unambiguous semidirect product	(C₃×C₇×C₂₉)⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₂₉	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₃²×C₁₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₂₉	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₃×C₂₉

48 conjugacy classes of subgroups.

μ_t(G) = 7917

5655 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23751, 13);