Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C79 · Schur multiplier (H2) = C214 |
| direct product | C2×C79×#3585 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C79 | C23×D4 |
| commutator, Frattini, cosocle | C4 | C26×C79 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C79 ◁ C22×#41×C79 ◁ G | |
11138 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 6 generators on 97 points:
(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(3,4)(5,9)(6,8)(7,10)(11,14)(12,16)(13,15)(17,18);(4,8)(6,14)(9,15)(10,11)(13,18)(16,17);(3,5)(4,9)(6,13)(7,12)(8,15)(10,16)(11,17)(14,18);(5,12)(9,16)(13,18)(15,17);(4,10)(8,11)(9,16)(15,17)6478 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 56076);