H(3,𝔽₅)×C₂₅₁ #44535899

order	31375
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₅²×C₂₅₁ · Schur multiplier (H₂) = C₅²

Aliases

direct product	H(3,𝔽₅)×C₂₅₁
unambiguous semidirect product	C₅²⋊(C₅×C₂₅₁)

	subgroup	G/H
center, socle	C₅×C₂₅₁	C₅²
commutator, Frattini, cosocle	C₅	C₅²×C₂₅₁
LCS	G ▷ C₅ ▷ C₁
UCS	C₁ ◁ C₅×C₂₅₁ ◁ G

30 conjugacy classes of subgroups.

7279 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31375, 3);