Finite Group DatabasebetaFinite Group Databasebeta| order | 28749 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C37 |
| unambiguous semidirect product | C7⋊#16861552 |
| Fitting, socle, derived, Hall | C7×C372 ⋊ C3 |
| Sylow | C372 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ #16861552 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C372 | C3 |
| LCS | G ▷ C7×C372 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 777 |
Polycyclic presentation:
3,7,37^2|b^a=b^2,c^a=c^26,d^a=d^103197 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28749, 15);