Finite Group DatabasebetaFinite Group Databasebeta| order | 13570 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C5×C23×D59 |
| unambiguous semidirect product | C59⋊(C2×C5×C23) |
| Fitting, socle, Hall | C5×C23×C59 ⋊ C2 |
| derived, Sylow | C59 ⋊ C2×C5×C23 |
| Hall | C23×C59 ⋊ C2×C5 |
| Hall | C5×C59 ⋊ C2×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C23 | D59 |
| commutator, cosocle, hypocenter | C59 | C2×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C59 | C2 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C5×C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6785 |
3565 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D23×D59, D5×C23×D59, D59×D115, … |
| maximal normal subgroup of | C5×D23×D59, D5×C23×D59, D59×D115, … |
| maximal quotient of | C5×C23×Dic59, C2×C5×C23×D59 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13570, 2);