Finite Group DatabasebetaFinite Group Databasebeta| order | 23571 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9×C97 · Schur multiplier (H2) = C34 |
| direct product | C9×H(3,𝔽3)×C97 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C97 | C32 |
| commutator | C3 | C32×C9×C97 |
| Frattini, cosocle | C32 | C33×C97 |
| socle | C32×C97 | C33 |
| prime radical | C3×H(3,𝔽3)×C97 | C3 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C97 ◁ G | |
202 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 7857 |
A minimal faithful permutation representation — 3 generators on 115 points:
(1,2,4,3,5,7,6,8,9)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(10,11,13)(12,15,17)(14,18,16);(11,14,15)(13,17,18)9603 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23571, 35);