Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#95×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2349 |
704 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,c^2=ef,b^a=be,c^a=cf,d^b=de,h^b=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35297949, #35297954, #35372106, … |
| maximal normal subgroup of | #35297949, #35297954, #35372106, … |
| maximal quotient of | #35325835, #35325838, #35325851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7417);