Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #391×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2715 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting | #391×C79 | C2 |
| prime radical | C22×D316 | C22 |
| hypercenter | #391 | D79 |
| hypocenter | C79 | #2715 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #391 | |
498 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^78,c^b=cg,d^b=de1124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34495649, #34495654, #34495755, … |
| maximal normal subgroup of | #34495649, #34495654, #34495755, … |
| maximal quotient of | #34215878, #34215969, #34216122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 11321);