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×#24422 |
| 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 | |
1300 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,6,12,8,11,7,4)(3,13,15,25,17,9,16,18)(5,20,21,26,22,10,23,19)(14,24,28,32,29,27,30,31)(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);(1,3,8,17)(2,9,11,13)(4,18,12,25)(5,14,22,29)(6,16,7,15)(10,24,20,27)(19,31,26,32)(21,30,23,28);(1,4)(2,7)(3,13)(5,19)(6,11)(8,12)(9,17)(10,21)(14,27)(15,18)(16,25)(20,23)(22,26)(24,29)(28,32)(30,31);(1,5)(2,10)(3,14)(4,19)(6,23)(7,21)(8,22)(9,24)(11,20)(12,26)(13,27)(15,30)(16,28)(17,29)(18,31)(25,32)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 17410);