Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C79 · Schur multiplier (H2) = C26 |
| direct product | C79×#33372 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | C22×#99 |
| commutator | C2×C4 | C23×C4×C79 |
| Frattini, cosocle | C2×Q8 | C24×C79 |
| prime radical | C79×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C2×D4×C79 ◁ C2×2−1+4×C79 ◁ G | |
1176 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,3,10,6,11,14,25)(4,8,12,24,15,22,26,32)(5,9,17,7,18,20,13,21)(16,23,29,19,28,31,27,30)(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);(1,3,6,14)(2,7,11,21)(4,12,15,26)(5,17,18,13)(8,19,22,30)(9,25,20,10)(16,29,28,27)(23,32,31,24);(1,4)(2,8)(3,12)(5,16)(6,15)(7,19)(9,23)(10,24)(11,22)(13,27)(14,26)(17,29)(18,28)(20,31)(21,30)(25,32);(4,15)(8,22)(12,26)(16,28)(19,30)(23,31)(24,32)(27,29)3634 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 26360);