Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4700 |
| Fitting | C2×C3×C4×C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×#443 |
472 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 189 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)(6,9,10,19,12,18,11,8)(7,14,15,21,16,13,20,17);(1,2)(6,8,11,18,12,19,10,9)(7,13,15,17,16,14,20,21);(4,5)(6,7)(8,17)(9,14)(10,15)(11,20)(12,16)(13,18)(19,21);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#67568, C2×#67441, #10704973, … |
| maximal normal subgroup of | C2×#67568, C2×#67441, #10704973, … |
| maximal quotient of | C2×C8×D24, C2×C8×#204, C2×C8×Dic12, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11052);