Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C61 · Schur multiplier (H2) = C25 |
| direct product | C61×#568 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C61 | C24 |
| commutator | C2 | C23×C4×C61 |
| Frattini, cosocle | C4 | C24×C61 |
| socle | C2×C61 | C23×C4 |
| prime radical | C2×#41×C61 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C61 ◁ G | |
258 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 976 |
A minimal faithful permutation representation — 4 generators on 77 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)(62,63,65,69,66,68,72,75)(64,67,71,74,70,73,76,77);(62,64)(63,67)(65,71)(66,70)(68,73)(69,74)(72,76)(75,77);(64,70)(67,73)(71,76)(74,77);(63,68)(67,73)(69,75)(74,77)2074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 249);