Finite Group DatabasebetaFinite Group Databasebeta| order | 10832 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14582142 |
| unambiguous semidirect product | (C2×#14582142)⋊C2 |
| Fitting | C22×C677 ⋊ C4 |
| Sylow | C677 ⋊ C22⋊C4 |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,677|a^2=d,b^a=bc,e^a=e^26,e^d=e^676686 conjugacy classes — view the full character table.
| maximal subgroup of | #36343504, #36343505, C2×C22⋊#14582142, … |
| maximal normal subgroup of | #36343504, #36343505, C2×C22⋊#14582142, … |
| maximal quotient of | (C2×#14582142)⋊C4, C22⋊#19129319, #36343503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10832, 45);