Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C313 · Schur multiplier (H2) = C1 |
| direct product | M32×C313 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C313 | C22 |
| commutator | C2 | C2×C8×C313 |
| Frattini, cosocle | C8 | C22×C313 |
| socle | C2×C313 | C2×C8 |
| prime radical | C22×C313 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C313 ◁ G | |
26 conjugacy classes of subgroups.
6260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×C313, #349×C313, #350×C313, … |
| maximal normal subgroup of | #347×C313, #349×C313, #350×C313, … |
| maximal quotient of | #346×C313, C22⋊C16×C313, C4⋊C16×C313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 17);