C₃×#11724369 #72228709

order	2592
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂²×C₃

Aliases

Fitting	C₂²×C₃⁴ ⋊ Q₈
Sylow	C₃⁴ ⋊ C₂²⋊Q₈

556 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

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

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 19 points:

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

maximal subgroup of	C₃×#67×PSU(3,𝔽₂)
maximal normal subgroup of	C₃×#67×PSU(3,𝔽₂)

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2,3)(4,5,6)(7,10,8,14)(9,15,13,11), (17,19), (5,6)(8,10,12,15)(9,13,14,11)(16,17)(18,19));