Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#4764 |
| Fitting | C2×C3×#102 ⋊ C2 |
| Sylow | C3 ⋊ C2×#490 |
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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:
(1,2)(3,4,5)(6,9,10,8)(7,12,13,11)(14,15)(16,21)(17,18)(19,20);(1,2)(6,8)(7,11)(9,10)(12,13)(15,19)(16,20)(18,21);(4,5)(6,7,10,13)(8,12,9,11)(15,18)(19,21);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4764, #10803257, #10803274, … |
| maximal normal subgroup of | C4×#4764, #10803257, #10803274, … |
| maximal quotient of | C2×#68849, C2×#70188, C2×#68856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11312);