Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C83 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C24×D83 |
| commutator, socle | C2×C83 | C24×C4 |
| Fitting, prime radical | #585×C83 | C2 |
| cosocle | C4×C83 | C25 |
| hypercenter | #585 | D83 |
| hypocenter | C83 | #3573 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C4 ◁ #585 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,f^2=g,h^a=h^82,e^b=eg,d^c=dg1462 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35410361, #35410367, #35410372, … |
| maximal normal subgroup of | #35410361, #35410367, #35410372, … |
| maximal quotient of | #36267825, #36267860, #36268041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 19222);