Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×#948 |
| Sylow | C3 ⋊ C4×#131 |
572 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 381 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(10,16)(13,19)(17,22)(20,23);(8,10)(9,13)(11,17)(12,16)(14,20)(15,19)(18,22)(21,23);(2,3)(8,9,11,14,12,15,18,21)(10,13,17,20,16,19,22,23);(4,5,6,7)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10685861, #10685866, #10685872, … |
| maximal normal subgroup of | #10685861, #10685866, #10685872, … |
| maximal quotient of | C8×#948, #10760799, #10760852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15086);