Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #548×D79 |
| Fitting | #548×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#548 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C25 |
| Fitting | #548×C79 | C2 |
| hypercenter | #548 | D79 |
| hypocenter | C79 | C2×#548 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ #548 | |
1620 conjugacy classes of subgroups.
1025 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3265×D79, #3269×D79, #3270×D79, … |
| maximal normal subgroup of | #3265×D79, #3269×D79, #3270×D79, … |
| maximal quotient of | Q8×C22⋊C4×D79, #2341×D79, #2351×D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17972);