Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Hall | C3×C19 ⋊ #127 |
| Sylow | C19 ⋊ #940 |
| Sylow | C3 ⋊ #10597386 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D19 |
| commutator, socle, cosocle | C22×C3×C19 | C23 |
| Fitting | C2×C3×C4×C19 | C22 |
| hypercenter | C2×C4 | D3×D19 |
| hypocenter | C3×C19 | #127 |
| LCS | G ▷ C22×C3×C19 ▷ C3×C19 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 912 |
Polycyclic presentation:
2^5,3,19|c^2=d,b^a=be,c^a=cd,g^a=g^18,c^b=cd,f^b=f^2186 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 597);