Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#983 |
| Fitting | C2×C4×Q8 ⋊ D3 |
278 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 20 points:
(5,7,14)(6,17,19,10,11,20)(9,15,16)(12,18);(5,6)(7,12)(8,11)(9,10)(13,17)(14,20)(15,18)(16,19);(1,2,3,4)52 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#983, #983⋊C8, #11711846, … |
| maximal normal subgroup of | C8×#983, #983⋊C8, #11711846, … |
| maximal quotient of | C8×#983, #11711846, #11711862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17903);