Finite Group DatabasebetaFinite Group Databasebeta| order | 1224 |
| isoclinism | isoclinic class of (C3⋊#595)⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊#595)⋊D3 |
| Fitting, socle, derived, Hall | C32×C17 ⋊ C2×C4 |
| Sylow | C17 ⋊ #624 |
| Sylow | C32 ⋊ C2×#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C17 | C2×C4 |
| prime radical | C3⋊D3×D17 | C2 |
| cosocle | C32×D17 | C22 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 102 |
Polycyclic presentation:
2^3,3^2,17|a^2=c,d^a=d^2,f^a=f^13,d^b=d^2,e^b=e^2,f^c=f^1642 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#595 |
| maximal normal subgroup of | D32×#595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1224, 131);