Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | C2×#4878 |
| Sylow | C3 ⋊ C2×#499 |
360 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(3,4,5)(6,8,9,13)(7,10,11,12)(15,20)(16,22)(17,25)(19,26)(23,24)(27,29);(14,16,17,23,18,24,25,22)(15,19,21,26,20,27,28,29);(4,5)(6,7,9,11)(8,12,13,10)(14,15)(16,19)(17,21)(18,20)(22,29)(23,26)(24,27)(25,28);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10713765, #10713767, #10713778, … |
| maximal normal subgroup of | #10713765, #10713767, #10713778, … |
| maximal quotient of | C2×#70607, C2×#68858, C2×#70611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11718);