Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#4991 |
| Fitting | C22×C3×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C2×#394 |
1252 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 261 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:
(1,2)(3,4,5)(10,12,13,11)(15,17);(6,7,8,9)(10,11)(12,13);(1,2)(4,5)(7,9)(14,15)(16,17);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10690199, #10690201, #10690204, … |
| maximal normal subgroup of | #10690199, #10690201, #10690204, … |
| maximal quotient of | C2×#69426, C2×#71570, C2×#69429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14764);