Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#4673 |
| Fitting | C2×C3×#95 ⋊ C2 |
| Sylow | C3 ⋊ C2×#393 |
1036 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 253 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) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,7,8,9)(11,13)(14,16)(15,19)(17,21)(18,20);(7,9)(10,11,12,13)(15,18)(16,21);(1,2)(4,5)(7,9)(11,13)(14,15)(16,20)(17,18)(19,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10690175, #10690190, #10695396, … |
| maximal normal subgroup of | #10690175, #10690190, #10695396, … |
| maximal quotient of | C2×#69428, C2×#69427, C2×#69413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5947);