Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#805 |
| Fitting | C22×C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ C22×#104 |
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(5,6,7)(9,12,13,14);(6,7)(8,9)(10,12)(11,13)(14,15);(3,4);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10700694, #10700700, #10700701, … |
| maximal normal subgroup of | #10700694, #10700700, #10700701, … |
| maximal quotient of | C22×#4459, C22×#4456, C2×#69734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14626);