Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#4553 |
| Sylow | C3 ⋊ C2×#349 |
236 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 109 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) = 96 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(7,11)(8,14)(13,18)(15,20);(4,5)(6,7,8,12,9,13,15,19,10,11,14,17,16,18,20,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10682153, #10682154, #10682155, … |
| maximal normal subgroup of | #10682153, #10682154, #10682155, … |
| maximal quotient of | C2×#67673, #10704249, C2×#67709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4554);