Finite Group DatabasebetaFinite Group Databasebeta| order | 3534 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C31 ⋊ C2×C3 |
| Hall | #13183714 ⋊ C2 |
| Hall | D589 ⋊ C3 |
| Sylow | C31 ⋊ D19⋊C3 |
| Sylow | C19 ⋊ D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C31 | C2×C3 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 589 |
Polycyclic presentation:
2,3,19,31|c^a=c^18,d^a=d^30,c^b=c^7,d^b=d^5104 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#16812976, C5⋊#16812976, #16812976⋊C5, … |
| maximal normal subgroup of | C5×#16812976, #16812976⋊C5, C7×#16812976 |
| maximal quotient of | C5×#16812976, C5⋊#16812976, C7×#16812976, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3534, 24);