Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2358 |
928 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=g,b^a=be,c^a=cf,d^b=de,h^b=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2358×D83, C2×#24910442, #35563963, … |
| maximal normal subgroup of | #2358×D83, C2×#24910442, #35563963, … |
| maximal quotient of | C22⋊C4×C22⋊Dic83, #35325897, #35325902, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7489);