Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#4651 |
| Sylow | C3 ⋊ C2×#383 |
624 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 624 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) = 384 |
A minimal faithful permutation representation — 4 generators on 25 points:
(3,4,5)(6,7,8,9)(10,12)(11,14)(13,16)(15,17)(18,20)(19,22)(21,25)(23,24);(1,2)(10,11,13,15)(12,14,16,17)(20,25)(22,24);(4,5)(12,16)(14,17)(18,19,21,23)(20,24,25,22);(1,2)96 conjugacy classes — view the full character table.
| maximal subgroup of | #10684809, #10685197, #10685225, … |
| maximal normal subgroup of | #10684809, #10685197, #10685225, … |
| maximal quotient of | C2×#69402, C2×#69401, C2×#69403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5900);