Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×C4⋊S4 |
| Fitting | C22×C42 ⋊ D3 |
433 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 433 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 12 points:
(5,6,7,8)(9,10,12);(6,8)(10,11);(1,2,3,4)56 conjugacy classes — view the full character table.
| maximal subgroup of | #11711105, #11711145, C4×#5415, … |
| maximal normal subgroup of | #11711105, #11711145, C4×#5415, … |
| maximal quotient of | C4×(C2×S4)⋊C4, C4×C4⋊SL(2,ℤ/4), #11711713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17864);