Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C22×#890 |
| Sylow | C3 ⋊ C22×#125 |
1192 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 645 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) = 384 |
A minimal faithful permutation representation — 5 generators on 23 points:
(1,2)(3,4)(5,6,7)(8,10,11,15)(9,12,13,14)(17,21)(18,22);(16,18,19,22)(17,20,21,23);(6,7)(8,9,11,13)(10,14,15,12)(16,17)(18,20)(19,21)(22,23);(3,4);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10687831, #10704101, #10704108, … |
| maximal normal subgroup of | #10687831, #10704101, #10704108, … |
| maximal quotient of | C22×#4977, C22×#4654, C22×#4655, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18278);