Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#834 |
| Sylow | C3 ⋊ C22×#99 |
1112 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 309 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)(8,9)(10,12)(11,13)(14,15);(6,7)(9,12,13,15)(10,14);(3,4);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10700529, #10700530, #10700574, … |
| maximal normal subgroup of | #10700529, #10700530, #10700574, … |
| maximal quotient of | C22×#4525, C22×#4528, C2×#71600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16616);