Finite Group DatabasebetaFinite Group Databasebeta| order | 8168 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1021 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #16861391 |
| commutator, hypocenter | C1021 | C8 |
| Fitting, socle | C2×C1021 | C4 |
| LCS | G ▷ C1021 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1021|a^2=b,b^2=c,d^a=d^374,d^b=d^1020518 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22551053, D1021⋊C8, #30654732, … |
| maximal normal subgroup of | C2×#22551053, D1021⋊C8, #30654732, … |
| maximal quotient of | #30654726, C2×#22551053 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8168, 13);