C₅²×C₁₇×C₁₉⋊C₃ #37564482

order	24225
automorphism	?
homology	Abelianization (H₁) = C₃×C₅²×C₁₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×C₁₇×C₁₉⋊C₃
unambiguous semidirect product	C₁₉⋊(C₃×C₅²×C₁₇)
unambiguous semidirect product	(C₅×C₁₉)⋊(C₃×C₅×C₁₇)
unambiguous semidirect product	(C₁₇×C₁₉)⋊(C₃×C₅²)
unambiguous semidirect product	(C₅×C₁₇×C₁₉)⋊(C₃×C₅)

	subgroup	G/H
center, hypercenter	C₅²×C₁₇	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃×C₅²×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₇×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₅²×C₁₇

64 conjugacy classes of subgroups.

μ_t(G) = 8075

3825 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24225, 6);