Finite Group DatabasebetaFinite Group Databasebeta| order | 35584 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C139 · Schur multiplier (H2) = C4 |
| direct product | C139×#7422 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C139 | #1347 |
| commutator | C2×C16 | C2×C4×C139 |
| Frattini, cosocle | C2×M32 | C22×C139 |
| prime radical | #2218×C139 | C2 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C139 ◁ C2×C4×C139 ◁ C22×C8×C139 ◁ C2×M32×C139 ◁ G | |
150 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 171 |
| transitive degree | μt(G) = 4448 |
A minimal faithful permutation representation — 2 generators on 171 points:
(1,2)(3,13,16,7)(4,18)(5,21)(6,12)(8,14,26,29)(9,19)(10,15)(11,22)(17,25,32,28)(20,27)(23,30,24,31)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171);(2,7)(3,14)(4,15)(5,22)(8,10)(9,26)(11,28)(12,13)(16,29)(17,31)(18,24)(19,20)(21,25)(23,27)(30,32)4309 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35584, 410);