Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×#117×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2324 |
668 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=ce1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35410123, #35410127, #35410153, … |
| maximal normal subgroup of | #35410123, #35410127, #35410153, … |
| maximal quotient of | #35325656, #35325696, #35325712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7203);