Finite Group DatabasebetaFinite Group Databasebeta| order | 1824 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C24×C19 ⋊ C2×C3 |
| Hall | #10597399 ⋊ C3 |
| Hall | C19⋊C3 ⋊ #120 |
| Sylow | C19 ⋊ C3×#120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D19⋊C3 |
| commutator, socle, cosocle | C22×C19 | C23×C3 |
| Fitting | C24×C19 | C2×C3 |
| hypercenter | C24 | D19⋊C3 |
| hypocenter | C19 | C3×#120 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ C24 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
Polycyclic presentation:
2^3,3,2^2,19|b^a=bf,c^a=ce,g^a=g^18,g^d=g^1190 conjugacy classes — view the full character table.
| maximal subgroup of | #120×D19⋊C3, #72241764, #72241772 |
| maximal normal subgroup of | #120×D19⋊C3, #72241764, #72241772 |
| maximal quotient of | #72241771, #72241799 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1824, 371);