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×#24474 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C79×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ G | |
1298 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,7,11,8,12,6,5)(3,13,15,9,17,24,16,25)(4,18,20,28,21,27,22,10)(14,30,31,26,32,23,19,29)(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)(4,19)(5,13)(6,16)(7,15)(8,17)(10,26)(11,24)(12,25)(14,20)(18,23)(21,31)(22,32)(27,30)(28,29);(1,4,8,21)(2,10,12,28)(3,14,17,32)(5,18,11,27)(6,20,7,22)(9,23,25,30)(13,29,24,26)(15,19,16,31);(1,5)(2,7)(3,13)(4,18)(6,12)(8,11)(9,15)(10,22)(14,29)(16,25)(17,24)(19,23)(20,28)(21,27)(26,32)(30,31)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 17462);