C₅×#64096 #13088070

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²×C₃

Aliases

Hall	C₃²×C₅ ⋊ C₄×Q₈
Sylow	C₃² ⋊ C₄×C₅×Q₈

420 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.

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

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 1440

A minimal faithful permutation representation — 3 generators on 23 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4387);