Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C26×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2846 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator, socle, cosocle | C23×C83 | C24 |
| Fitting | C26×C83 | C2 |
| hypercenter | C26 | D83 |
| hypocenter | C83 | #2846 |
| LCS | G ▷ C23×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ C26 | |
3422 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^a=be,c^a=cf,d^a=dg,h^a=h^822668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35435981, #35435983, #35436848, … |
| maximal normal subgroup of | #35435981, #35435983, #35436848, … |
| maximal quotient of | #35335560, #35335613, #35335619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12787);