Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D11×#64418 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D11×#64418 |
| commutator, cosocle, hypocenter | C11×#3862 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C11 | C2×D3 |
| LCS | G ▷ C11×#3862 | |
| UCS | C1 ◁ C5 | |
136 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 770 |
700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 320);