Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4894 |
| Fitting | C2×C3×#108 ⋊ C2 |
| Sylow | C3 ⋊ C2×#444 |
464 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 464 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)(6,9,10,19,12,20,11,13)(7,8,14,16,15,18,21,17);(1,2)(6,8,11,17,12,18,10,16)(7,13,14,9,15,19,21,20);(4,5)(6,7)(8,9)(10,14)(11,21)(12,15)(13,17)(16,19)(18,20);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10710477, #10710479, #10710484, … |
| maximal normal subgroup of | #10710477, #10710479, #10710484, … |
| maximal quotient of | C2×#68558, C2×#68517, C2×#68518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11824);