C₂⁴×C₅²⋊C₃ #11925820

order	1200
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶×C₅

Aliases

C₂⁴×C₅²⋊C₃

Fitting, socle, Hall	C₂⁴×C₅² ⋊ C₃
derived, Sylow	C₅² ⋊ C₂⁴×C₃

	subgroup	G/H
center, hypercenter	C₂⁴	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂⁴×C₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₅²	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂⁴

402 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 4 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 1030);