C₃×D₁₃⋊M₁₆ #11929169

order	1248
isoclinism	isoclinic class of #6118
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₃×D₁₃⋊M₁₆

Hall	C₃×C₁₃ ⋊ C₂×M₁₆
Sylow	C₁₃ ⋊ C₂×C₃×M₁₆

136 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 312

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 1281);