Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C42×C313 ⋊ C2 |
| Sylow | C313 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D313 |
| commutator, socle, cosocle | C22×C313 | C23 |
| Fitting | C42×C313 | C2 |
| prime radical | C22×D313 | C22 |
| hypercenter | C42 | D313 |
| hypocenter | C313 | #126 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ C42 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^3122510 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D313, C2×#23756491, #34094685, … |
| maximal normal subgroup of | #126×D313, C2×#23756491, #34094685, … |
| maximal quotient of | #34094020, #34094036, #34094043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 140);