Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #585×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3584 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×C22⋊D79 |
| commutator, cosocle | C4×C79 | C25 |
| Frattini | C4 | C24×D79 |
| Fitting | #585×C79 | C2 |
| socle | C2×C79 | C23×D4 |
| hypercenter | #585 | D79 |
| hypocenter | C79 | #3584 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C4 ◁ C2×#41 ◁ #585 | |
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,h^b=h^78,d^c=dg1370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34304222, #34304225, #34304233, … |
| maximal normal subgroup of | #34304222, #34304225, #34304233, … |
| maximal quotient of | #35151832, #35151834, #35151945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19281);