Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C313 ⋊ #125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D313 |
| commutator, socle, prime radical, cosocle | C22×C313 | C23 |
| Fitting | C4⋊C4×C313 | C2 |
| hypercenter | C4⋊C4 | D313 |
| hypocenter | C313 | #125 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=d,b^2=e,c^2=d,b^a=bd,c^a=ce,f^b=f^312,f^c=f^3121574 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34094450, #34094451, #34094454, … |
| maximal normal subgroup of | #34094450, #34094451, #34094454, … |
| maximal quotient of | #34094017, #34094035, #34094039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 137);