Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#19097683 |
| Fitting | C22×C8×C157 ⋊ C2 |
| Sylow | C157 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2536 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34098059, #34099893, C4×#19097683, … |
| maximal normal subgroup of | #34098059, #34099893, C4×#19097683, … |
| maximal quotient of | C2×#23756996, C2×#23756998, #34098448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 509);