C₂⁵×C₁₃⋊C₃ #11929340

order	1248
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂⁵×C₁₃⋊C₃

Fitting, socle, Hall	C₂⁵×C₁₃ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₂⁵×C₃

	subgroup	G/H
center, hypercenter	C₂⁵	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂⁵×C₃
Frattini	C₁	G
Fitting, socle	C₂⁵×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁵

1496 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 5 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1452);