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×SD64 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | D16 |
| commutator, Frattini, cosocle | C16 | C22×C61 |
| prime radical | D16×C61 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C4×C61 ◁ C8×C61 ◁ C16×C61 ◁ G | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 2 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)(62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(63,77)(64,92)(65,75)(66,90)(67,73)(68,88)(69,71)(70,86)(72,84)(74,82)(76,80)(79,93)(81,91)(83,89)(85,87)1159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 53);