Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4895 |
| Fitting | C2×C3×#108 ⋊ C2 |
| Sylow | C3 ⋊ C2×#443 |
472 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 472 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) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(6,9,10,19,11,17,20,12)(7,13,14,21,16,8,15,18);(1,2)(6,8,10,18,11,13,20,21)(7,12,15,17,16,19,14,9);(4,5)(6,7)(8,17)(9,13)(10,14)(11,16)(12,18)(15,20)(19,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10710420, #10710422, #10710427, … |
| maximal normal subgroup of | #10710420, #10710422, #10710427, … |
| maximal quotient of | C2×#68556, C2×#68516, C2×#68557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11823);