Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | #379×C83 ⋊ C2 |
| Sylow | C83 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^a=be,c^a=cf,d^b=de,h^d=h^821198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35419722, #35419724, #35420530, … |
| maximal normal subgroup of | #35419722, #35419724, #35420530, … |
| maximal quotient of | #35325803, #35325807, #35325816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7326);