Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D83 |
| commutator | C22×C83 | C23×C4 |
| Fitting, prime radical | C22×#41×C83 | C2 |
| socle, cosocle | C23×C83 | C24 |
| hypercenter | C22×#41 | D83 |
| hypocenter | C83 | #2311 |
| LCS | G ▷ C22×C83 ▷ C83 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
880 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=ce1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309732, #35309734, #35309797, … |
| maximal normal subgroup of | #35309732, #35309734, #35309797, … |
| maximal quotient of | #35325656, #35325706, #35325713, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7102);