Finite Group DatabasebetaFinite Group Databasebeta| order | 18564 |
| automorphism | ? |
| homology | Abelianization (H1) = C17 · Schur multiplier (H2) = C2 |
| direct product | C17×PSL(2,𝔽13) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C17 | PSL(2,𝔽13) |
| commutator, hypocenter | PSL(2,𝔽13) | C17 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽13) | |
| UCS | C1 ◁ C17 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 238 |
A minimal faithful permutation representation — 2 generators on 31 points:
(18,20,27)(21,28,31)(22,23,25)(24,29,30);(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,22)(21,23)(25,29)(26,30)(28,31)153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18564, 237);