Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×#19099399 |
| Fitting | C22×#41×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#585 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D79 |
| commutator, cosocle | C2×C79 | C26 |
| Frattini | C2 | C25×D79 |
| Fitting | C22×#41×C79 | C2 |
| socle | C22×C79 | C25 |
| hypercenter | C22×#41 | D79 |
| hypocenter | C79 | C2×#585 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2×C4 ◁ C22×#41 | |
5956 conjugacy classes of subgroups.
1628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34287520, #34287521, #34287522, … |
| maximal normal subgroup of | #34287520, #34287521, #34287522, … |
| maximal quotient of | C2×#23776599, C2×#23776601, C2×#23776603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19318);