Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4783 |
| Fitting | C2×C3×#102 ⋊ C2 |
| Sylow | C3 ⋊ C2×#452 |
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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)(12,19)(14,22)(15,23)(18,25)(20,21);(1,2)(6,7)(8,9)(10,12)(11,15)(13,20)(14,19)(16,18)(17,25)(21,22)(23,24);(4,5)(6,7)(8,9)(10,11)(12,18)(13,16)(14,17)(15,20)(19,23)(21,25)(22,24);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10800812, C4×#4783, #10800886, … |
| maximal normal subgroup of | #10800812, C4×#4783, #10800886, … |
| maximal quotient of | C2×#68294, C2×#68298, C2×#68287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11322);