Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#826 |
| Fitting | C3×C4×D8 ⋊ C2 |
| Sylow | C3 ⋊ C4×D16 |
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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 — 3 generators on 23 points:
(1,2,3)(9,13)(10,17)(11,18)(14,15)(16,22)(19,23)(20,21);(2,3)(8,9)(10,13)(11,20)(12,16)(14,17)(15,18)(19,22)(21,23);(4,5,6,7)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10706906, C8×#826, #10706935, … |
| maximal normal subgroup of | #10706906, C8×#826, #10706935, … |
| maximal quotient of | C8×#826, #10707080, #10707082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3459);