C₅×C₃⋊(D₁₃⋊C₃) #11924059

order	1170
isoclinism	isoclinic class of C₃⋊(D₁₃⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₃⋊(D₁₃⋊C₃)
unambiguous semidirect product	C₃⋊(C₅×D₁₃⋊C₃)
unambiguous semidirect product	(C₁₃⋊C₃)⋊(C₅×D₃)
unambiguous semidirect product	D₃₉⋊(C₃×C₅)
unambiguous semidirect product	(C₅×D₃₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₅	C₃⋊(D₁₃⋊C₃)
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃	C₂×C₃
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₅

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 195

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1170, 17);