Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5050 |
| Sylow | C3 ⋊ C2×#451 |
740 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 181 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:
(1,2)(3,4,5)(7,9)(10,13,15,12)(11,17,19,25)(14,20,24,22)(16,23,21,18);(1,2)(6,7)(8,9)(10,12)(11,16)(13,15)(14,20)(17,18)(19,21)(22,24)(23,25);(4,5)(10,11,15,19)(12,16,13,21)(14,23,24,18)(17,20,25,22);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10690315, #10690317, #10691624, … |
| maximal normal subgroup of | #10690315, #10690317, #10691624, … |
| maximal quotient of | C2×#69701, C2×#69716, C2×#69707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15316);