Finite Group DatabasebetaFinite Group Databasebeta| order | 35028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| Fitting, socle | C3×C7×C139 ⋊ C22×C3 |
| derived | C3×C139 ⋊ C22×C3×C7 |
| Hall | C3×C7×C139⋊C3 ⋊ C22 |
| Hall | C3×C139⋊C3 ⋊ C22×C7 |
| Hall | C7×C139 ⋊ C2×C3×D3 |
| Sylow | C139 ⋊ C2×C3×D3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D3×D139⋊C3 |
| commutator, cosocle, hypocenter | C3×C139 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C139 | C22×C3 |
| LCS | G ▷ C3×C139 | |
| UCS | C1 ◁ C7 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 149 |
| transitive degree | μt(G) = 2919 |
A minimal faithful permutation representation — 2 generators on 149 points:
(1,2,3)(4,5,6,7,8,9,10)(12,16,17,13,14,18)(15,24,25,19,20,34)(21,37,38,27,28,51)(22,36,32,30,26,23)(29,56,57,40,41,74)(31,54,55,43,39,48)(33,35,53,45,46,49)(42,79,80,59,60,103)(44,77,78,62,58,71)(47,52,76,64,65,72)(50,92,90,68,69,67)(61,108,109,82,83,132)(63,106,107,85,81,100)(66,75,105,87,88,101)(70,119,120,93,94,96)(73,123,117,97,98,91)(84,124,122,99,111,142)(86,135,136,112,110,129)(89,104,134,114,115,130)(95,137,141,113,121,125)(102,144,139,126,127,118)(116,133,143,128,138,148)(131,149,147,145,146,140);(2,3)(11,12,15,21,29,42,61,84,97,65,28,39,49,51,71,96,122,143,149,138,83,110,121,124,127,130,132,141,107,57,76,92,77,56,75,102,128,114,87,64,45,32,17,16,22,31,44,63,86,113,93,68,46,20,26,34,48,67,91,118,140,145,115,60,81,94,98,101,103,129,136,80,105,123,119,106,79,104,131,147,139,117,90,55,25,36,24,35,50,70,95,112,85,62,43,30,14,18,23,33,47,66,89,116,126,88,41,58,69,72,74,100,125,109,134,144,111,137,135,108,133,146,148,142,120,78,38,53,54,37,52,73,99,82,59,40,27,19,13)609 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35028, 122);