Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2396 |
528 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^82,c^b=cg,h^b=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35411890, #35411891, #35411901, … |
| maximal normal subgroup of | #35411890, #35411891, #35411901, … |
| maximal quotient of | #35326115, #35326117, #35326133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7786);