Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×C11×#64418 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C11 | #64418 |
| commutator, cosocle, hypocenter | #3862 | C22×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C72×C11 | D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C2×C5×C11 | |
136 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1540 |
2200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 462);