Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×Q64 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C61 | D16 |
| commutator, Frattini, cosocle | C16 | C22×C61 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C4×C61 ◁ C8×C61 ◁ C16×C61 ◁ G | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 3904 |
A minimal faithful permutation representation — 2 generators on 125 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61)(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)(94,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95);(62,94,78,110)(63,95,79,111)(64,96,80,112)(65,97,81,113)(66,98,82,114)(67,99,83,115)(68,100,84,116)(69,101,85,117)(70,102,86,118)(71,103,87,119)(72,104,88,120)(73,105,89,121)(74,106,90,122)(75,107,91,123)(76,108,92,124)(77,109,93,125)1159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 54);