Finite Group DatabasebetaFinite Group Databasebeta| order | 10832 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C677 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #14582142 |
| commutator, hypocenter | C677 | C16 |
| Fitting | C4×C677 | C4 |
| socle, prime radical | C2×C677 | C8 |
| cosocle | #19129312 | C2 |
| LCS | G ▷ C677 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,677|a^2=b,b^2=c,c^2=d,e^a=e^26,e^b=e^676692 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#24925394, D677⋊C16, #36343520, … |
| maximal normal subgroup of | C2×#24925394, D677⋊C16, #36343520, … |
| maximal quotient of | #36343496, C2×#24925394 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10832, 43);