Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#5405 |
| Fitting | C2×#131 ⋊ D3 |
255 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 34 points:
(3,11,28,10,18,26,15,31,17,4,13,33,8,21,30,20,6,25,5,23,19,9,29,34)(7,12,14,24,16,22,27,32);(4,9)(6,7)(10,20)(11,22)(12,21)(13,14)(16,18)(17,19)(23,32)(24,31)(27,29)(28,30);(1,2)52 conjugacy classes — view the full character table.
| maximal subgroup of | #11711564, #11712583, C4×#5405, … |
| maximal normal subgroup of | #11711564, #11712583, C4×#5405, … |
| maximal quotient of | C2×GL(2,𝔽3)⋊C8, C2×#226⋊C8, #11711829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18023);