Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D632 |
| Fitting | C23×C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C23×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D316 |
| commutator, cosocle | C4×C79 | C25 |
| Frattini | C4 | C24×D79 |
| Fitting | C23×C8×C79 | C2 |
| socle | C24×C79 | D4 |
| hypercenter | C23×C8 | D79 |
| hypocenter | C79 | C23×D8 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1976 conjugacy classes of subgroups.
2552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34195067, #34195069, #34195093, … |
| maximal normal subgroup of | #34195067, #34195069, #34195093, … |
| maximal quotient of | C23×#14579083, C23×#14579095, C22×C4×D632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19226);