Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#19098356 |
| Sylow | C79 ⋊ C2×#353 |
368 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34176008, #34176009, #34176032, … |
| maximal normal subgroup of | #34176008, #34176009, #34176032, … |
| maximal quotient of | C2×#23761332, C2×#23761346, #34197539, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6168);