Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#362 |
| Fitting | C3×#362 ⋊ C2 |
| Sylow | C3 ⋊ C2×#362 |
216 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,3,6,15)(2,7,11,24)(4,17,19,30)(5,20,21,14)(8,25,27,28)(9,23,10,22)(12,16,29,26)(13,18,31,32)(33,34,35);(1,2,5,9,6,11,21,10)(3,12,14,25,15,29,20,28)(4,16,18,8,19,26,32,27)(7,17,22,13,24,30,23,31);(34,35)48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#362, D3×#2148, #10948155, … |
| maximal normal subgroup of | C2×D3×#362, D3×#2148, #10948155, … |
| maximal quotient of | D3×#1334, #10704964, #10705195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1841);