Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#5113 |
| Fitting | C23×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×#416 |
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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) = 192 |
A minimal faithful permutation representation — 4 generators on 25 points:
(3,4,5)(7,9)(10,12,13,18,14,19,20,24)(11,15,16,21,17,22,23,25);(1,2)(10,11,14,17)(12,15,19,22)(13,16,20,23)(18,21,24,25);(4,5)(6,7)(8,9)(12,18)(13,20)(15,21)(16,23)(19,24)(22,25);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10700687, #10700693, #10700708, … |
| maximal normal subgroup of | #10700687, #10700693, #10700708, … |
| maximal quotient of | C2×#69734, C2×#70763, #10761600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16315);