Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #433×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3224 |
408 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|b^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^82,c^b=ce,d^b=dg,f^c=fg,h^c=h^821174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3224×D83, C2×#24918559, #36275815, … |
| maximal normal subgroup of | #3224×D83, C2×#24918559, #36275815, … |
| maximal quotient of | #35413780, #35414169, #35415015, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 15606);