C₅×C₇⋊(C₇⋊C₈) #14519945

order	1960
isoclinism	isoclinic class of C₇⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₅×C₈ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₅×C₇⋊(C₇⋊C₈)
unambiguous semidirect product	C₇⋊(C₅×C₇⋊C₈)

derived, Sylow	C₇² ⋊ C₅×C₈
Hall	C₅×C₇² ⋊ C₈

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1960

A minimal faithful permutation representation — 3 generators on 27 points:

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

520 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1960, 42);