Finite Group DatabasebetaFinite Group Databasebeta| order | 5529 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C97 ⋊ C3 |
| Sylow | C97 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ C97⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C97 | C3 |
| LCS | G ▷ C19×C97 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
3,19,97|b^a=b^7,c^a=c^35617 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#19149507, #26010884, #26010888, … |
| maximal normal subgroup of | C2×#19149507, #26010884, #26010888, … |
| maximal quotient of | C2×#19149507, #30658671, C3×#19149507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5529, 3);