Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C4×C3⋊C8 |
| Sylow | C3 ⋊ C8×C22⋊C4 |
384 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 181 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 | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(12,13,14,16,15,17,18,19);(1,2,3)(9,11);(4,5,6,7)(8,9)(10,11)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10685727, C3⋊C8×#99, #10685737, … |
| maximal normal subgroup of | #10685727, C3⋊C8×#99, #10685737, … |
| maximal quotient of | C3⋊C8×C22⋊C8, #10685662, #10685678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2022);