Finite Group DatabasebetaFinite Group Databasebeta| order | 1560 |
| isoclinism | isoclinic class of Q8⋊(C13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| Fitting, Hall | C5×Q8×C13 ⋊ C3 |
| derived, Hall | Q8×C13 ⋊ C3×C5 |
| Hall | C5×C13 ⋊ SL(2,𝔽3) |
| Hall | C5×Q8 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ C5×SL(2,𝔽3) |
| Sylow | Q8 ⋊ C5×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C22⋊(C13⋊C3) |
| commutator, cosocle, hypocenter | Q8×C13 | C3×C5 |
| Frattini | C2 | C5×C22⋊(C13⋊C3) |
| Fitting | C5×Q8×C13 | C3 |
| socle | C2×C5×C13 | A4 |
| LCS | G ▷ Q8×C13 | |
| UCS | C1 ◁ C2×C5 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 520 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1560, 107);