Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #407×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2975 |
452 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,f^2=g,b^a=be,c^a=cg,d^a=deg,c^b=ceg,h^c=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298417, #35298420, #35299375, … |
| maximal normal subgroup of | #35298417, #35298420, #35299375, … |
| maximal quotient of | #35403080, #35403081, #35403150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13549);