Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C72×PSL(2,𝔽11) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C72 | PSL(2,𝔽11) |
| commutator, hypocenter | PSL(2,𝔽11) | C72 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽11) | |
| UCS | C1 ◁ C72 | |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 539 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,3,4,5,6,7)(8,9,10,11,12,13,14)(15,17,19,20,21,25,23,18,22,16,24);(8,9,10,11,12,13,14)(15,17,20)(16,18,22)(21,23,24)392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 660);