Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C83 ⋊ #1440 |
736 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,c^2=d,b^a=bd,c^a=ce,c^b=cf,h^c=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296977, #1440×D83, C2×#24905710, … |
| maximal normal subgroup of | #35296977, #1440×D83, C2×#24905710, … |
| maximal quotient of | #35292326, #35292327, #35292329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2757);