C₁₇×D₁₃ #89212

order	442
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₁₃
unambiguous semidirect product	C₁₃⋊(C₂×C₁₇)

Fitting, socle, Hall	C₁₃×C₁₇ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₁₇

	subgroup	G/H
center, hypercenter	C₁₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₇

8 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 221

A minimal faithful permutation representation — 2 generators on 30 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30);(1,2,4,6,8,10,12,13,11,9,7,5,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(442, 1);