Finite Group DatabasebetaFinite Group Databasebeta| order | 35148 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic8787 |
| unambiguous semidirect product | C3⋊Dic2929 |
| derived, Hall | C3×C29×C101 ⋊ C4 |
| Hall | C29×C101 ⋊ Dic3 |
| Hall | C3×C101 ⋊ Dic29 |
| Sylow | C101 ⋊ Dic87 |
| Hall | C3×C29 ⋊ Dic101 |
| Sylow | C29 ⋊ Dic303 |
| Sylow | C3 ⋊ Dic2929 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D8787 |
| commutator, hypocenter | C3×C29×C101 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C29×C101 | C2 |
| LCS | G ▷ C3×C29×C101 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 35148 |
A minimal faithful permutation representation — 2 generators on 137 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)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137);(1,3,2,4)(6,7)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(38,137)(39,136)(40,135)(41,134)(42,133)(43,132)(44,131)(45,130)(46,129)(47,128)(48,127)(49,126)(50,125)(51,124)(52,123)(53,122)(54,121)(55,120)(56,119)(57,118)(58,117)(59,116)(60,115)(61,114)(62,113)(63,112)(64,111)(65,110)(66,109)(67,108)(68,107)(69,106)(70,105)(71,104)(72,103)(73,102)(74,101)(75,100)(76,99)(77,98)(78,97)(79,96)(80,95)(81,94)(82,93)(83,92)(84,91)(85,90)(86,89)(87,88)Polycyclic presentation:
2,3,29,101,2|a^2=e,b^a=b^2,c^a=c^28,d^a=d^1008790 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35148, 8);