Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19099304 |
| Fitting | C2×#126×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#560 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D79 |
| commutator, cosocle | C22×C79 | C25 |
| Frattini | C22 | C24×D79 |
| Fitting | C2×#126×C79 | C2 |
| socle | C23×C79 | C24 |
| hypercenter | C2×#126 | D79 |
| hypocenter | C79 | C2×#560 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ C2×#126 | |
1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34450956, C4×#19099304, #34454073, … |
| maximal normal subgroup of | #34450956, C4×#19099304, #34454073, … |
| maximal quotient of | C2×#23766540, C2×#23766547, C2×#23766553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18628);