C₂×C₈₉×(C₅⋊D₅)⋊C₃ #40998931

order	26700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₈₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₈₉×(C₅⋊D₅)⋊C₃
unambiguous semidirect product	(C₂×C₅⋊D₅)⋊(C₃×C₈₉)
unambiguous semidirect product	(C₂×C₅⋊D₅×C₈₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₈₉	(C₅⋊D₅)⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂²×C₃×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₈₉	C₂×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₈₉

60 conjugacy classes of subgroups.

μ_t(G) = 2670

1780 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26700, 74);