C₇×D₅⋊C₁₆ #11764641

order	1120
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×D₅⋊C₁₆
unambiguous semidirect product	D₅⋊(C₇×C₁₆)

derived, Sylow	C₅ ⋊ C₂×C₇×C₁₆
Hall	C₅×C₇ ⋊ C₂×C₁₆

56 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 560

A minimal faithful permutation representation — 2 generators on 28 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 247);