Finite Group DatabasebetaFinite Group Databasebeta| order | 1268 |
| isoclinism | isoclinic class of #11929639 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C317 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C317 | C4 |
| prime radical, cosocle | D317 | C2 |
| LCS | G ▷ C317 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 317 |
| transitive degree | μt(G) = 317 |
Polycyclic presentation:
2^2,317|a^2=b,c^a=c^203,c^b=c^31683 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11929639, C3×#11929639, C3⋊#11929639, … |
| maximal normal subgroup of | C2×#11929639, C3×#11929639, C11×#11929639, … |
| maximal quotient of | #14579268, C2×#11929639, C3×#11929639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1268, 3);