Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C83 ⋊ #1311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4×C8 | C2×D83 |
| commutator | C2×C83 | C82 |
| Fitting | C82×C83 | C2 |
| socle, prime radical | C22×C83 | C4×C8 |
| cosocle | C4×C8×C83 | C22 |
| hypercenter | C82 | D83 |
| hypocenter | C83 | #1311 |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C4×C8 ◁ C82 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=bg,h^a=h^822704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35291021, #35291070, #35291071, … |
| maximal normal subgroup of | #35291021, #35291070, #35291071, … |
| maximal quotient of | #35291019, #35291232, #35291734, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2427);