Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#19097751 |
| Fitting | C2×C4⋊C4×C157 ⋊ C2 |
| Sylow | C157 ⋊ C2×C22⋊Q8 |
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34100442, #34100447, #34100558, … |
| maximal normal subgroup of | #34100442, #34100447, #34100558, … |
| maximal quotient of | C2×#23757130, C2×#23757147, C2×#23757158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1048);