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 ⋊ #2554 |
560 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,b^2=eg,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^821678 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2554×D83, C2×#24912517, #35574588, … |
| maximal normal subgroup of | #2554×D83, C2×#24912517, #35574588, … |
| maximal quotient of | #35326702, #35326861, #35327642, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 9564);