C₁₇×C₁₉×C₅²⋊C₃ #37564480

order	24225
automorphism	?
homology	Abelianization (H₁) = C₃×C₁₇×C₁₉ · Schur multiplier (H₂) = C₅

Aliases

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

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

24 conjugacy classes of subgroups.

μ_t(G) = 4845

3553 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24225, 4);