Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#4690 |
| Fitting | C2×C3×C4×C8 ⋊ 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)(14,16,17,22,18,23,24,28)(15,20,21,27,19,25,26,29);(1,2)(6,8,9,12)(7,10,11,13)(15,19)(20,25)(21,26)(27,29);(4,5)(6,7)(8,10)(9,11)(12,13)(14,15)(16,20)(17,21)(18,19)(22,27)(23,25)(24,26)(28,29);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10685724, #10685726, #10688053, … |
| maximal normal subgroup of | #10685724, #10685726, #10688053, … |
| maximal quotient of | C2×#69751, C2×#69753, C2×#69755, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11030);