Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C4×C313 ⋊ C4 |
| Sylow | C313 ⋊ #117 |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=e,c^2=d,b^a=bd,f^a=f^25,f^e=f^312644 conjugacy classes — view the full character table.
| maximal subgroup of | #34095019, #34095020, #34095023, … |
| maximal normal subgroup of | #34095019, #34095020, #34095023, … |
| maximal quotient of | #34095088, C4×C22⋊#11929411, C4×C4⋊#11929411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 225);