Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #568×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D79 |
| commutator, socle | C2×C79 | C24×C4 |
| Fitting | #568×C79 | C2 |
| prime radical | #19099399 | C2 |
| cosocle | C4×C79 | C25 |
| hypercenter | #568 | D79 |
| hypocenter | C79 | #3573 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C4 ◁ #568 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,f^2=g,h^a=h^78,e^b=eg,d^c=dg,h^e=h^781394 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34294228, #34294230, #34294234, … |
| maximal normal subgroup of | #34294228, #34294230, #34294234, … |
| maximal quotient of | #35151691, #35151692, #35151693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19223);