Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4542 |
| Sylow | C3 ⋊ C2×#355 |
260 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 260 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) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 21 points:
(3,4,5)(6,8)(7,12)(9,11)(10,18)(13,14)(15,21)(16,19)(17,20);(4,5)(6,7,9,13,11,15,8,16)(10,19,17,12,20,14,18,21);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10682932, #10682933, #10682956, … |
| maximal normal subgroup of | #10682932, #10682933, #10682956, … |
| maximal quotient of | C2×#67640, C2×#67632, #10704461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4309);