Finite Group DatabasebetaFinite Group Databasebeta| order | 1368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Hall | C32×C19 ⋊ D4 |
| Sylow | C19 ⋊ #638 |
| Sylow | C32 ⋊ D76 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D3×D19 |
| commutator, Fitting, socle, cosocle | C2×C32×C19 | C22 |
| hypocenter | C32×C19 | D4 |
| LCS | G ▷ C2×C32×C19 ▷ C32×C19 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 684 |
Polycyclic presentation:
2^3,3^2,19|b^2=c,b^a=bc,f^a=f^18,d^b=d^2,e^b=e^2129 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1368, 112);