Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 7053312 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C16×C83 |
| multiplicative | (ℤ/22712)ˣ, (ℤ/32064)ˣ, (ℤ/34068)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C24×C83 |
| socle, prime radical | C24×C83 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
440 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, 2136);