Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #578×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3584 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D4×D79 |
| commutator, cosocle | C4×C79 | C25 |
| Frattini | C4 | C24×D79 |
| Fitting | #578×C79 | C2 |
| socle | C2×C79 | C23×D4 |
| hypercenter | #578 | D79 |
| hypocenter | C79 | #3584 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #578 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,d^c=dg,h^c=h^78,h^d=h^78,h^e=h^78902 conjugacy classes — view the full character table.
| maximal subgroup of | #34442222, #34442228, #34442251, … |
| maximal normal subgroup of | #34442222, #34442228, #34442251, … |
| maximal quotient of | #35151831, #35151946, #35152385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19280);