Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C22×#898 |
| Fitting | C22×C3×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C22×#126 |
1320 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 565 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 — 5 generators on 23 points:
(1,2)(3,4)(5,6,7)(8,10,11,14)(9,13,12,15)(17,21)(20,23);(9,12)(10,14)(16,18,19,22)(17,20,21,23);(6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,20)(19,21)(22,23);(3,4);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10686550, #10687837, #10687839, … |
| maximal normal subgroup of | #10686550, #10687837, #10687839, … |
| maximal quotient of | C22×#4651, C22×#4978, C22×#4654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18279);