Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C25 |
| direct product | C79×#25446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #2428 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ G | |
876 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,7,11,8,12,6,4)(3,13,16,25,17,18,15,9)(5,20,22,26,23,19,21,10)(14,28,30,32,31,24,29,27)(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)(2,9,12,25)(4,18,11,13)(5,14)(6,15)(7,16)(8,17)(10,24,26,28)(19,32,20,27)(21,29)(22,30)(23,31);(1,4)(2,6)(3,13)(5,19)(7,12)(8,11)(9,16)(10,21)(14,27)(15,25)(17,18)(20,23)(22,26)(24,30)(28,29)(31,32);(1,5,6,21,8,23,7,22)(2,10,11,20,12,26,4,19)(3,14,15,29,17,31,16,30)(9,24,13,27,25,28,18,32)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 18434);