Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#4458 |
| Sylow | C3 ⋊ C2×#335 |
200 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(14,15,19,21,17,20,16,18);(4,5)(6,7,8,10,9,11,12,13)(15,18)(16,19)(20,21);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10682056, #10682057, #10682068, … |
| maximal normal subgroup of | #10682056, #10682057, #10682068, … |
| maximal quotient of | C2×#67654, C4×#4458, #10688026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2304);