C₅×C₂²⋊(C₇⋊C₈) #11764501

order	1120
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₅×C₂²⋊(C₇⋊C₈)
unambiguous semidirect product	C₂²⋊(C₅×C₇⋊C₈)

Hall	C₅×C₇ ⋊ C₂²⋊C₈
Sylow	C₇ ⋊ C₅×C₂²⋊C₈

100 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 560

A minimal faithful permutation representation — 2 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 107);