C₂×C₅×D₁₅×C₈₉ #40999002

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

Aliases

direct product	C₂×C₅×D₁₅×C₈₉
unambiguous semidirect product	(C₂×C₃)⋊(C₅×D₅×C₈₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₅×D₃×C₈₉)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₈₉	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₅×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₈₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅×C₈₉

96 conjugacy classes of subgroups.

μ_t(G) = 5340

8010 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26700, 145);