Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5143 |
| Sylow | C3 ⋊ C2×#473 |
448 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2)(3,4,5)(7,13)(9,22)(12,26)(14,16)(15,29)(17,31)(19,35)(23,34)(24,30)(27,28)(32,33)(36,37);(1,2)(6,8,18,25,11,21,10,20)(7,12,24,33,16,28,15,17)(9,19,34,37,22,35,23,36)(13,26,30,32,14,27,29,31);(4,5)(6,7,11,16)(8,17,21,33)(9,13,22,14)(10,24,18,15)(12,25,28,20)(19,31,35,32)(23,30,34,29)(26,37,27,36);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10712157, #10712159, #10712206, … |
| maximal normal subgroup of | #10712157, #10712159, #10712206, … |
| maximal quotient of | C2×#70850, C2×#70852, C2×#70854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16385);