Finite Group DatabasebetaFinite Group Databasebeta| order | 28749 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C7×C1369 ⋊ C3 |
| Sylow | C1369 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C1369⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C1369 | C3 |
| Frattini | C37 | #11715912 |
| socle | C7×C37 | C37⋊C3 |
| LCS | G ▷ C7×C1369 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9583 |
Polycyclic presentation:
3,7,37^2|c^37=d^30,b^a=b^2,c^a=c^10d,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, 4);