Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#5001 |
| Fitting | C2×C3×#117 ⋊ C2 |
| Sylow | C3 ⋊ C2×#418 |
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 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) = 17 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(6,8,9,7)(10,11)(12,17)(13,15)(14,16);(1,2)(11,15)(14,17);(4,5)(6,7)(8,9)(11,14)(12,16)(15,17);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10700672, #10700674, #10700731, … |
| maximal normal subgroup of | #10700672, #10700674, #10700731, … |
| maximal quotient of | C2×#70756, C2×#70799, #10761627, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14788);