Finite Group DatabasebetaFinite Group Databasebeta| order | 8264 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C1033 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1033 | C8 |
| LCS | G ▷ C1033 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1033|a^2=b,b^2=c,d^a=d^802,d^b=d^678,d^c=d^1032137 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22551925 |
| maximal normal subgroup of | C2×#22551925 |
| maximal quotient of | #30658337, C2×#22551925 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8264, 15);