Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C313 · Schur multiplier (H2) = C2 |
| direct product | #104×C313 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C313 | D4 |
| commutator | C4 | C2×C4×C313 |
| Frattini, cosocle | C2×C4 | C22×C313 |
| socle | C2×C313 | C22⋊C4 |
| prime radical | #41×C313 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C313 ◁ C2×C4×C313 ◁ G | |
44 conjugacy classes of subgroups.
4382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#104×C313, #421×C313, #443×C313, … |
| maximal normal subgroup of | C2×#104×C313, #421×C313, #443×C313, … |
| maximal quotient of | D4⋊C8×C313, Q8⋊C8×C313, #327×C313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 11);