Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#4709 |
| Fitting | C2×C3×#97 ⋊ C2 |
| Sylow | C3 ⋊ C2×#433 |
412 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 189 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) = 192 |
A minimal faithful permutation representation — 4 generators on 29 points:
(3,4,5)(7,11)(10,13)(14,16,17,23,18,22,24,28)(15,20,21,27,19,25,26,29);(1,2)(6,8,9,12)(7,10,11,13)(15,19)(16,22)(21,26)(23,28);(4,5)(6,7)(8,10)(9,11)(12,13)(14,15)(16,20)(17,21)(18,19)(22,25)(23,27)(24,26)(28,29);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10685722, #10688055, #10793329, … |
| maximal normal subgroup of | #10685722, #10688055, #10793329, … |
| maximal quotient of | C2×#69806, C2×#69830, C2×#69832, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11064);