Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5416943616 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C29×C4 |
| abelian | C23×C42×C83 |
| multiplicative | (ℤ/40080)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C22 | C25×C83 |
| socle, prime radical | C25×C83 | C22 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
3000 conjugacy classes of subgroups.
10624 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2150);