Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C61 | C22 |
| commutator | C2 | C22×C8×C61 |
| Frattini, cosocle | C8 | C23×C61 |
| socle | C2×C61 | C22×C8 |
| prime radical | #41×C61 | C4 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C61 ◁ G | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 93 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)(62,63,65,69,66,70,75,81,67,71,76,82,77,83,87,91)(64,68,73,79,74,80,86,90,72,78,84,88,85,89,92,93);(62,64)(63,68)(65,73)(66,74)(67,72)(69,79)(70,80)(71,78)(75,86)(76,84)(77,85)(81,90)(82,88)(83,89)(87,92)(91,93);(64,72)(68,78)(73,84)(74,85)(79,88)(80,89)(86,92)(90,93)2440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 185);