C₃²×C₁₃×C₂₉⋊C₇ #37557653

order	23751
automorphism	?
homology	Abelianization (H₁) = C₃²×C₇×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₁₃×C₂₉⋊C₇
unambiguous semidirect product	C₂₉⋊(C₃²×C₇×C₁₃)
unambiguous semidirect product	(C₃×C₂₉)⋊(C₃×C₇×C₁₃)
unambiguous semidirect product	(C₃²×C₂₉)⋊(C₇×C₁₃)
unambiguous semidirect product	(C₃²×C₁₃×C₂₉)⋊C₇

	subgroup	G/H
center, hypercenter	C₃²×C₁₃	C₂₉⋊C₇
commutator, cosocle, hypocenter	C₂₉	C₃²×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₂₉	C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₃²×C₁₃

48 conjugacy classes of subgroups.

μ_t(G) = 3393

1287 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23751, 11);