Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C313 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #11929411 |
| commutator, hypocenter | C313 | C32 |
| Fitting | C8×C313 | C4 |
| socle, prime radical | C2×C313 | C16 |
| cosocle | #19097536 | C2 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^25,f^b=f^312656 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#23756547, #34095083, #34095084, … |
| maximal normal subgroup of | C2×#23756547, #34095083, #34095084, … |
| maximal quotient of | #34094991, C2×#23756547 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 196);