Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C313 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14578818 |
| commutator, socle | C2×C313 | C2×C8 |
| Fitting, prime radical | C22×C313 | C8 |
| cosocle | #14578816 | C22 |
| hypercenter | C22 | #14578818 |
| hypocenter | C313 | M32 |
| LCS | G ▷ C2×C313 ▷ C313 | |
| UCS | C1 ◁ C2 ◁ C22 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^5,f^c=f^25,f^d=f^312176 conjugacy classes — view the full character table.
| maximal subgroup of | #34095250, #34095251, C2×#23756593, … |
| maximal normal subgroup of | #34095250, #34095251, C2×#23756593, … |
| maximal quotient of | #34095246, C22⋊#19097573, #34095255, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 242);