C₅²×C₂₃×C₁₃⋊C₃ #36375815

order	22425
automorphism	?
homology	Abelianization (H₁) = C₃×C₅²×C₂₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×C₂₃×C₁₃⋊C₃
unambiguous semidirect product	C₁₃⋊(C₃×C₅²×C₂₃)
unambiguous semidirect product	(C₅×C₁₃)⋊(C₃×C₅×C₂₃)
unambiguous semidirect product	(C₁₃×C₂₃)⋊(C₃×C₅²)
unambiguous semidirect product	(C₅×C₁₃×C₂₃)⋊(C₃×C₅)

	subgroup	G/H
center, hypercenter	C₅²×C₂₃	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₅²×C₂₃
Frattini	C₁	G
Fitting, socle	C₅²×C₁₃×C₂₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅²×C₂₃

64 conjugacy classes of subgroups.

μ_t(G) = 7475

4025 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22425, 6);