C₈₉×H(3,𝔽₅) #26013259

order	11125
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₅²×C₈₉ · Schur multiplier (H₂) = C₅²

Aliases

direct product	C₈₉×H(3,𝔽₅)
unambiguous semidirect product	C₅²⋊(C₅×C₈₉)
unambiguous semidirect product	(C₅²×C₈₉)⋊C₅

	subgroup	G/H
center, socle	C₅×C₈₉	C₅²
commutator, Frattini, cosocle	C₅	C₅²×C₈₉
LCS	G ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₅×C₈₉ ◁ G

30 conjugacy classes of subgroups.

2581 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11125, 3);