Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C26 |
| direct product | C79×#24420 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ G | |
1326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,5,11,7,8,6,12)(3,13,17,22,16,24,14,9)(4,18,19,26,20,10,21,25)(15,27,28,23,29,32,30,31)(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);(2,8)(3,14)(5,6)(9,13)(10,18)(15,28)(16,17)(19,21)(22,24)(23,27)(29,30)(31,32);(1,3)(2,9)(4,15)(5,14)(6,17)(7,16)(8,22)(10,23)(11,24)(12,13)(18,31)(19,30)(20,29)(21,28)(25,27)(26,32);(1,4)(2,10)(3,15)(5,21)(6,19)(7,20)(8,18)(9,23)(11,26)(12,25)(13,27)(14,28)(16,29)(17,30)(22,31)(24,32)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 17408);