Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#4717 |
| Fitting | C2×C3×#97 ⋊ C2 |
| Sylow | C3 ⋊ C2×#444 |
464 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 464 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)(6,9,10,17,11,18,19,8)(7,12,13,20,15,21,14,16);(1,2)(6,8,10,9,11,17,19,18)(7,12,14,16,15,21,13,20);(4,5)(6,7)(8,16)(9,12)(10,13)(11,15)(14,19)(17,20)(18,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10710480, #10710482, #10710487, … |
| maximal normal subgroup of | #10710480, #10710482, #10710487, … |
| maximal quotient of | C2×#68076, C2×#68084, C2×#68077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11081);