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×#24473 |
| 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 | |
1314 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,6,11,8,12,7,5)(3,13,17,25,18,15,16,9)(4,19,22,28,23,27,21,10)(14,24,20,26,30,32,31,29)(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)(4,20)(5,15)(6,17)(7,16)(8,18)(10,26)(11,13)(12,25)(14,21)(19,32)(22,30)(23,31)(24,27)(28,29);(1,4)(2,10)(3,14)(5,19)(6,21)(7,22)(8,23)(9,24)(11,27)(12,28)(13,29)(15,26)(16,20)(17,31)(18,30)(25,32);(1,5,8,11)(2,7,12,6)(3,15,18,13)(4,19,23,27)(9,16,25,17)(10,22,28,21)(14,26,30,29)(20,32,31,24)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 17461);