Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #387×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×C22⋊Q8 |
656 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=e,d^2=eg,b^a=be,c^a=cf,h^b=h^82,h^c=h^82,h^d=h^821204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C22⋊Q8×D83, C2×#24909997, C4×#19128209, … |
| maximal normal subgroup of | C4×C22⋊Q8×D83, C2×#24909997, C4×#19128209, … |
| maximal quotient of | #35325570, #35325576, #387×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7044);