Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×D4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2972 |
500 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,f^2=g,b^a=be,d^a=de,c^b=ce,h^d=h^821708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35373835, #35373837, #35373839, … |
| maximal normal subgroup of | #35373835, #35373837, #35373839, … |
| maximal quotient of | #35403074, #35403132, #35403289, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13531);