Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#5069 |
| Sylow | C3 ⋊ C2×#491 |
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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:
(3,4,5)(6,8,9,13)(7,11,10,12)(14,16)(15,19)(17,26)(18,23)(20,29)(21,28)(22,25)(24,27);(1,2)(6,7,9,10)(8,12,13,11)(16,23)(19,28)(22,29)(24,26);(4,5)(7,10)(11,12)(14,15,18,21)(16,22,23,29)(17,25,27,20)(19,26,28,24);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10690129, #10690131, #10696498, … |
| maximal normal subgroup of | #10690129, #10690131, #10696498, … |
| maximal quotient of | C2×#69548, C2×#69616, C2×#69552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15587);