Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×#876 |
| Fitting | C3×C43 ⋊ C2 |
| Sylow | C3 ⋊ C4×#126 |
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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)(9,13)(12,15)(16,18,19,23)(17,21,20,22);(8,10,11,14)(9,12,13,15)(17,20)(21,22);(2,3)(8,9)(10,12)(11,13)(14,15)(16,17)(18,22)(19,20)(21,23);(4,5,6,7)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10803397, C8×#876, #10803404, … |
| maximal normal subgroup of | #10803397, C8×#876, #10803404, … |
| maximal quotient of | C4×#4940, C4×#4933, C4×#4937, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5879);