Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1438 |
1168 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,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 | #35296973, #1438×D83, C2×#24905702, … |
| maximal normal subgroup of | #35296973, #1438×D83, C2×#24905702, … |
| maximal quotient of | #35292325, #35292326, #35292330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2749);