Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#19097836 |
| Fitting | C2×Q8×C157 ⋊ C4 |
| Sylow | C157 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
418 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#19097836, #34115900, #34115913, … |
| maximal normal subgroup of | C4×#19097836, #34115900, #34115913, … |
| maximal quotient of | C2×#23758121, C2×Q8⋊#11929441, #34115430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1545);