Finite Group DatabasebetaFinite Group Databasebeta| order | 1624 |
| isoclinism | isoclinic class of D29 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×Dic29 |
| derived, Sylow | C29 ⋊ C2×C4×C7 |
| Hall | C7×C29 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C7 | D29 |
| commutator, hypocenter | C29 | C2×C4×C7 |
| Frattini | C2 | C2×C7×D29 |
| Fitting, socle, prime radical | C22×C7×C29 | C2 |
| cosocle | C2×C29 | C22×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C22×C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1624 |
448 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1624, 28);