C₅×C₇⋊C₂₇ #11745698

order	945
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₅×C₂₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₇⋊C₂₇
unambiguous semidirect product	C₇⋊(C₅×C₂₇)
unambiguous semidirect product	(C₅×C₇)⋊C₂₇

derived, Sylow	C₇ ⋊ C₅×C₂₇
Hall	C₅×C₇ ⋊ C₂₇

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 945

A minimal faithful permutation representation — 2 generators on 39 points:

(1,2,3,4,5)(7,8,9)(10,12,11)(13,14,17,15,18,23,20,25,30,16,19,24,21,26,31,28,33,36,22,27,32,29,34,37,35,38,39);(6,7,8,10,9,11,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(945, 1);