Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4563 |
| Sylow | C3 ⋊ C2×#361 |
256 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 256 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)(7,12)(8,10)(9,16)(13,21)(14,20)(15,17)(18,19);(4,5)(6,7,8,13,11,15,10,20)(9,17,16,21,19,12,18,14);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4563, Dic3×#361, #10710457, … |
| maximal normal subgroup of | C4×#4563, Dic3×#361, #10710457, … |
| maximal quotient of | C2×#67762, #10704962, #10705193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4610);