Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#5211 |
| Sylow | C3 ⋊ C2×#381 |
1144 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 389 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) = 192 |
A minimal faithful permutation representation — 4 generators on 21 points:
(3,4,5)(6,7)(8,9)(10,11)(12,13)(14,16,17,20)(15,19,18,21);(1,2)(14,15)(16,19)(17,18)(20,21);(4,5)(7,9)(10,11,12,13)(15,18)(19,21);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10684798, #10684800, C2×#67616, … |
| maximal normal subgroup of | #10684798, #10684800, C2×#67616, … |
| maximal quotient of | C2×#72127, C2×#71534, C4×#5211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16602);