Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×#948 |
| Sylow | C3 ⋊ C22×#131 |
1504 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 1077 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 23 points:
(1,2)(3,4)(5,6,7)(8,10)(9,13)(11,17)(12,16)(14,20)(15,19)(18,22)(21,23);(10,16)(13,19)(17,22)(20,23);(6,7)(8,9,11,14,12,15,18,21)(10,13,17,20,16,19,22,23);(3,4);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10700599, #10700603, #10700619, … |
| maximal normal subgroup of | #10700599, #10700603, #10700619, … |
| maximal quotient of | C22×#4997, C2×C4×#948, C22×#5234, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19828);