C₂×C₃⁴⋊C₅ #11717696

order	810
isoclinism	isoclinic class of C₃⁴⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₃²

Aliases

direct product	C₂×C₃⁴⋊C₅
unambiguous semidirect product	(C₂×C₃⁴)⋊C₅

Fitting, socle, Hall	C₂×C₃⁴ ⋊ C₅
derived, Sylow	C₃⁴ ⋊ C₂×C₅

	subgroup	G/H
center, hypercenter	C₂	C₃⁴⋊C₅
commutator, cosocle, hypocenter	C₃⁴	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃⁴	C₅
LCS	G ▷ C₃⁴
UCS	C₁ ◁ C₂

92 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 30

A minimal faithful permutation representation — 2 generators on 17 points:

(1,2)(3,4,6,10,13)(5,8,12,14,17)(7,11,15,16,9);(3,5,9)(4,8,7)(10,15,14)(13,16,17)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(810, 103);