Finite Group DatabasebetaFinite Group Databasebeta| order | 35072 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C137 · Schur multiplier (H2) = C23 |
| direct product | C137×#10211 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C137 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C137 |
| prime radical | C23×C137 | #127 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G | |
406 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 201 |
| transitive degree | μt(G) = 8768 |
A minimal faithful permutation representation — 3 generators on 201 points:
(1,2,9,15)(3,16,22,30)(4,23,27,18)(5,28,33,51)(6,34,39,47)(7,17,41,53)(8,14,37,50)(10,42,20,24)(11,44,48,32)(12,38,52,64)(13,31,54,57)(19,55,46,63)(21,45,56,62)(25,61,40,35)(26,59,60,29)(36,58,49,43)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201);(1,3,8,21)(2,4,14,26)(5,29,32,18)(6,35,38,19)(7,10,31,43)(9,22,37,56)(11,45,28,16)(12,49,47,24)(13,40,53,63)(15,27,50,60)(17,55,54,25)(20,57,58,41)(23,33,59,44)(30,48,62,51)(34,42,52,36)(39,61,64,46);(1,4,8,26)(2,10,14,43)(3,17,21,54)(5,30,32,62)(6,36,38,42)(7,40,31,63)(9,27,37,60)(11,46,28,61)(12,29,47,18)(13,22,53,56)(15,20,50,58)(16,44,45,33)(19,51,35,48)(23,52,59,34)(24,39,49,64)(25,57,55,41)3425 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35072, 3199);