Finite Group DatabasebetaFinite Group Databasebeta| order | 17324 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×Dic61 |
| derived, Sylow | C61 ⋊ C4×C71 |
| Hall | C61×C71 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C71 | D61 |
| commutator, hypocenter | C61 | C4×C71 |
| Frattini | C2 | C71×D61 |
| Fitting, socle, prime radical | C2×C61×C71 | C2 |
| cosocle | C2×C61 | C2×C71 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C71 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17324 |
4544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17324, 2);