Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #213 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×#214 |
| Sylow | C3 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3)(13,16)(14,19)(17,18);(2,3)(12,13,15,18)(14,16,19,17);(4,5,6,8,7,9,10,11)96 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#214, #10706956, #10706958, … |
| maximal normal subgroup of | C16×#214, #10706956, #10706958, … |
| maximal quotient of | C8×#832, C8×#810, C8×#808, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3421);