Finite Group DatabasebetaFinite Group Databasebeta| order | 1029 |
| isoclinism | isoclinic class of #11759986 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C73 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C73 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 | |
232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 343 |
Polycyclic presentation:
3,7^3|b^a=b^4,c^a=c^4,d^a=d^4117 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#3861, #72228735, #72228751, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×#3861, #72228735, #72228751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1029, 17);