Finite Group DatabasebetaFinite Group Databasebeta| order | 17214 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#22575305 |
| Fitting, socle, Hall | C2×C19×C151 ⋊ C3 |
| derived, Hall | C19×C151 ⋊ C2×C3 |
| Hall | C2×C151 ⋊ C19⋊C3 |
| Sylow | C151 ⋊ C2×C19⋊C3 |
| Hall | C2×C19 ⋊ C151⋊C3 |
| Sylow | C19 ⋊ C2×C151⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22575305 |
| commutator, cosocle, hypocenter | C19×C151 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C151 | C3 |
| LCS | G ▷ C19×C151 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5738 |
1918 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22575305, #46806311, #46806315, … |
| maximal normal subgroup of | C4×#22575305, #46806311, #46806315, … |
| maximal quotient of | C4×#22575305, C22×#22575305 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17214, 4);