Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#5416 |
301 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 301 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 22 points:
(3,4,6)(7,9,11,17)(8,12,14,21)(10,19,20,16)(13,22,18,15);(4,5)(7,8,11,14)(9,15,17,22)(10,18,20,13)(12,19,21,16);(1,2)38 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#5416, #11712809, #11713061, … |
| maximal normal subgroup of | C4×#5416, #11712809, #11713061, … |
| maximal quotient of | C2×#73093, C2×#73095, C2×#73098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18073);