Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C83 · Schur multiplier (H2) = C22 |
| direct product | C83×#1333 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | #102 |
| commutator | C8 | C2×C8×C83 |
| Frattini, cosocle | C4×C8 | C22×C83 |
| prime radical | C2×D8×C83 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C42×C83 ◁ C4×C8×C83 ◁ G | |
108 conjugacy classes of subgroups.
2656 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 65);