Finite Group DatabasebetaFinite Group Databasebeta| order | 1029 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Sylow | H(3,𝔽7) ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C7 | #3862 |
| commutator, Fitting, cosocle, hypocenter | H(3,𝔽7) | C3 |
| LCS | G ▷ H(3,𝔽7) | |
| UCS | C1 ◁ C7 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 49 |
Polycyclic presentation:
3,7^3|b^a=b^4,c^a=b^2c^2d^6,c^b=cd37 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1029, 12);