Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C61 · Schur multiplier (H2) = C22 |
| direct product | C61×#464 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C61 |
| prime radical | C2×D4×C61 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C42×C61 ◁ G | |
112 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1952 |
A minimal faithful permutation representation — 3 generators on 81 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)(63,65)(66,67)(68,74)(69,71)(70,78)(72,76)(73,77)(75,81)(79,80);(62,63,64,65)(67,71)(72,80)(73,78)(74,81);(66,68,69,75)(67,72,71,80)(70,79,77,76)(73,81,78,74)1159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 145);