Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#5570 |
| Sylow | C3 ⋊ C2×#557 |
1048 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 581 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 — 5 generators on 21 points:
(1,2)(3,4,5)(6,8,9,13)(7,10,11,12);(14,17,18,21)(15,19,16,20);(14,16,18,15)(17,19,21,20);(4,5)(6,7,9,11)(8,12,13,10)(14,15,18,16)(17,19,21,20);(1,2)90 conjugacy classes — view the full character table.
| maximal subgroup of | #10686924, #10686933, #10686936, … |
| maximal normal subgroup of | #10686924, #10686933, #10686936, … |
| maximal quotient of | C2×Q8×C4⋊Dic3, C2×#82461, C2×#73640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18373);