Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23990 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C79 · Schur multiplier (H2) = C26 |
| direct product | C79×#23993 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C79 |
| prime radical | C79×#3021 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C4×C79 ◁ G | |
1152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 4 generators on 111 points:
(1,2,5,7)(3,8,13,20)(4,14,15,9)(6,18,17,10)(11,21,19,23)(12,22,26,27)(16,24,29,28)(25,31,30,32)(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);(2,7)(3,11,13,19)(8,21,20,23)(9,14)(10,18)(12,25,26,30)(22,31,27,32)(24,28);(1,3)(2,8)(4,12)(5,13)(6,19)(7,20)(9,22)(10,21)(11,17)(14,27)(15,26)(16,30)(18,23)(24,31)(25,29)(28,32);(1,4)(2,9)(3,12)(5,15)(6,16)(7,14)(8,22)(10,24)(11,25)(13,26)(17,29)(18,28)(19,30)(20,27)(21,31)(23,32)3160 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 16981);