Finite Group DatabasebetaFinite Group Databasebeta| order | 1029 |
| isoclinism | isoclinic class of #11759980 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C72 |
No aliases for this group.
| Fitting, derived, Sylow | H(3,𝔽7) ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | H(3,𝔽7) | C3 |
| Frattini, socle | C7 | #3861 |
| LCS | G ▷ H(3,𝔽7) | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 49 |
Polycyclic presentation:
3,7^3|b^a=b^2,c^a=c^2d^6,d^a=d^4,c^b=cd21 conjugacy classes — view the full character table.
| maximal subgroup of | #72209730 |
| maximal normal subgroup of | #72209730 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1029, 11);