Finite Group DatabasebetaFinite Group Databasebeta| order | 29728 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#21418261 |
| unambiguous semidirect product | #16836500⋊C8 |
| Fitting | C4×C929 ⋊ C8 |
| derived, Sylow | C929 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #21418261 |
| commutator, hypocenter | C929 | C4×C8 |
| Frattini | C2 | C2×#21418261 |
| Fitting | C4×C929 | C8 |
| socle | C2×C929 | C2×C8 |
| prime radical | C2×D929 | C2×C4 |
| cosocle | C2×#16836500 | C22 |
| LCS | G ▷ C929 | |
| UCS | C1 ◁ C4 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3716 |
496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29728, 237);