Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4809 |
| Fitting | C2×C3×#103 ⋊ C2 |
| Sylow | C3 ⋊ C2×#451 |
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 173 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)(6,8,9,7)(11,16)(12,18)(14,21)(15,22)(19,20)(23,25);(1,2)(6,7)(8,9)(10,12,13,19)(11,15,16,23)(14,18,21,20)(17,25,24,22);(4,5)(6,7)(8,9)(10,11)(12,15)(13,16)(14,17)(18,25)(19,23)(20,22)(21,24);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10800786, C4×#4809, #10800860, … |
| maximal normal subgroup of | #10800786, C4×#4809, #10800860, … |
| maximal quotient of | C2×#68318, C2×#68322, C2×#68327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11368);