Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D313 |
| unambiguous semidirect product | C313⋊C25 |
| unambiguous semidirect product | (C2×C313)⋊C24 |
| Fitting, socle | C24×C313 ⋊ C2 |
| derived, Sylow | C313 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D313 |
| commutator, cosocle, hypocenter | C313 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C313 | C2 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
2528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34094007, C2×C22⋊C4×D313, C22×#19097538, … |
| maximal normal subgroup of | #34094007, C2×C22⋊C4×D313, C22×#19097538, … |
| maximal quotient of | C23×C4×D313, C24×Dic313, C22×D4×D313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 195);