Finite Group DatabasebetaFinite Group Databasebeta| order | 8368 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C523 · Schur multiplier (H2) = C1 |
| direct product | M16×C523 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C523 | C22 |
| commutator | C2 | C2×C4×C523 |
| Frattini | C4 | C22×C523 |
| socle | C2×C523 | C2×C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C523 ◁ G | |
20 conjugacy classes of subgroups.
5230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8368, 6);