Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4790 |
| Sylow | C3 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 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) = 25 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(3,4,5)(6,8,9,7)(12,18)(13,21)(15,22)(16,25)(19,20)(23,24);(1,2)(10,12,14,20)(11,15,17,24)(13,18,21,19)(16,22,25,23);(4,5)(6,7,9,8)(10,11,14,17)(12,15,20,24)(13,16,21,25)(18,22,19,23);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4790, #10793685, #10793712, … |
| maximal normal subgroup of | C4×#4790, #10793685, #10793712, … |
| maximal quotient of | C2×#68213, C2×#68218, C2×#68219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11347);