Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×D8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #3322 |
414 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^82,c^b=cg,d^b=de,h^b=h^82,f^c=fg,h^d=h^821177 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3322×D83, C2×#24919669, #36281353, … |
| maximal normal subgroup of | #3322×D83, C2×#24919669, #36281353, … |
| maximal quotient of | #35420009, #35420843, #35421635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 16716);