Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of D48 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4904 |
| Fitting | C22×C3×C16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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:
(3,4,5)(6,9,20,34,11,22,25,35,12,23,18,31,8,17,10,21)(7,14,24,30,13,27,29,33,16,28,37,36,26,32,15,19);(1,2)(6,8,12,11)(7,13,16,26)(9,17,23,22)(10,18,25,20)(14,27,28,32)(15,24,29,37)(19,30,33,36)(21,31,35,34);(4,5)(6,7)(8,13)(9,19)(10,24)(11,26)(12,16)(14,21)(15,20)(17,30)(18,29)(22,36)(23,33)(25,37)(27,31)(28,35)(32,34);(1,2)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10712236, #10712238, #10712271, … |
| maximal normal subgroup of | #10712236, #10712238, #10712271, … |
| maximal quotient of | C2×#71412, C2×#71404, C2×C4×D48, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14579);