C₅×#6487 #11765082

order	1120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₅×C₇ ⋊ C₂²⋊Q₈
Sylow	C₇ ⋊ C₅×C₂²⋊Q₈

148 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

A minimal faithful permutation representation — 3 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 688);