C₃²×C₇×C₁₃×D₂₃ #49179239

order	37674
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₇×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₇×C₁₃×D₂₃
unambiguous semidirect product	C₂₃⋊(C₂×C₃²×C₇×C₁₃)

	subgroup	G/H
center, hypercenter	C₃²×C₇×C₁₃	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂×C₃²×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₃×C₂₃	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₃²×C₇×C₁₃

96 conjugacy classes of subgroups.

μ_t(G) = 18837

10647 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37674, 122);