Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C83 ⋊ C4×#126 |
516 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=ef,c^2=e,d^2=g,b^a=be,c^a=cf,h^a=h^82,h^c=h^82,h^d=h^821204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#126×D83, C2×#24910017, C4×#19128228, … |
| maximal normal subgroup of | C4×#126×D83, C2×#24910017, C4×#19128228, … |
| maximal quotient of | #388×Dic83, #35325565, #35325576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7064);