Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C26 |
| direct product | C79×#24475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C79×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ G | |
1324 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,7,11,8,13,6,12)(3,14,17,9,18,27,24,28)(4,19,21,29,5,23,22,10)(15,30,20,32,31,25,16,26)(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);(1,3)(2,9)(4,20)(5,16)(6,24)(7,17)(8,18)(10,26)(11,27)(12,14)(13,28)(15,22)(19,30)(21,31)(23,25)(29,32);(1,4,8,5)(2,10,13,29)(3,15,18,31)(6,21,7,22)(9,25,28,30)(11,23,12,19)(14,26,27,32)(16,24,20,17);(1,5,8,4)(2,10,13,29)(3,16,18,20)(6,21,7,22)(9,26,28,32)(11,19,12,23)(14,25,27,30)(15,24,31,17)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 17463);