Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#4966 |
| Fitting | C22×C3×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C2×#417 |
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 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) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(6,8,9,7)(11,14)(12,17)(15,16);(1,2)(10,12,13,17)(11,14,16,15);(4,5)(6,7)(8,9)(10,11)(12,14)(13,16)(15,17);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10700662, #10700664, #10700705, … |
| maximal normal subgroup of | #10700662, #10700664, #10700705, … |
| maximal quotient of | C2×#70425, C2×#70497, #10761646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14712);