Finite Group DatabasebetaFinite Group Databasebeta| order | 10832 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D677⋊C8 |
| derived, Sylow | C677 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14582142 |
| commutator, hypocenter | C677 | C2×C8 |
| Frattini | C2 | C2×#14582142 |
| Fitting | C4×C677 | C4 |
| socle | C2×C677 | C2×C4 |
| prime radical | C2×D677 | C4 |
| cosocle | Dic677 | C22 |
| LCS | G ▷ C677 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,677|a^2=c,c^2=d,e^a=e^26,e^b=e^676,e^c=e^676692 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14582142, #36343500, #36343508, … |
| maximal normal subgroup of | C8×#14582142, #36343500, #36343508, … |
| maximal quotient of | C4×#19129319, #36343503, #36343513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10832, 48);