C₁₇×C₂⁴⋊C₅ #13062866

order	1360
isoclinism	isoclinic class of C₂⁴⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₅×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₁₇×C₂⁴⋊C₅
unambiguous semidirect product	C₂⁴⋊(C₅×C₁₇)
unambiguous semidirect product	(C₂⁴×C₁₇)⋊C₅

Fitting, socle, Hall	C₂⁴×C₁₇ ⋊ C₅
derived, Sylow	C₂⁴ ⋊ C₅×C₁₇

	subgroup	G/H
center, hypercenter	C₁₇	C₂⁴⋊C₅
commutator, cosocle, hypocenter	C₂⁴	C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₇	C₅
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₁₇

34 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 170

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,23,25)(20,22,24,26,27);(18,20)(25,27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 234);