Finite Group DatabasebetaFinite Group Databasebeta| order | 1396 |
| isoclinism | isoclinic class of #13063703 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C349 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C349 | C4 |
| prime radical, cosocle | D349 | C2 |
| LCS | G ▷ C349 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 349 |
| transitive degree | μt(G) = 349 |
Polycyclic presentation:
2^2,349|a^2=b,c^a=c^213,c^b=c^34891 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13063703, #13063703⋊C3, C3×#13063703, … |
| maximal normal subgroup of | C2×#13063703, #13063703⋊C3, C3×#13063703, … |
| maximal quotient of | #14584102, C2×#13063703, C3×#13063703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1396, 3);