Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#14579083 |
| Fitting | C23×C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C22×#102 |
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34193832, #34193836, #34194530, … |
| maximal normal subgroup of | #34193832, #34193836, #34194530, … |
| maximal quotient of | C22×#19098292, C2×#23761826, C2×#23761800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 12997);