Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4566 |
| Sylow | C3 ⋊ C2×#360 |
232 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 93 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 — 3 generators on 21 points:
(3,4,5)(6,7)(8,15)(9,18)(10,12)(11,19)(13,17)(14,20)(16,21);(4,5)(7,11,12,20)(8,14)(9,17)(13,15,18,21)(16,19);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4566, Dic3×#360, #10710478, … |
| maximal normal subgroup of | C4×#4566, Dic3×#360, #10710478, … |
| maximal quotient of | C2×#67762, C2×#67764, #10704958, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4651);