Finite Group DatabasebetaFinite Group Databasebeta| order | 19690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D9845 |
| unambiguous semidirect product | C5⋊D1969 |
| unambiguous semidirect product | C11⋊D895 |
| unambiguous semidirect product | C179⋊D55 |
| Fitting, socle, derived, Hall | C5×C11×C179 ⋊ C2 |
| Hall | C11×C179 ⋊ D5 |
| Hall | C5×C179 ⋊ D11 |
| Sylow | C179 ⋊ D55 |
| Hall | C5×C11 ⋊ D179 |
| Sylow | C11 ⋊ D895 |
| Sylow | C5 ⋊ D1969 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C179 | C2 |
| LCS | G ▷ C5×C11×C179 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 195 |
| transitive degree | μt(G) = 9845 |
A minimal faithful permutation representation — 2 generators on 195 points:
(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195);(2,5)(3,4)(7,16)(8,15)(9,14)(10,13)(11,12)(18,195)(19,194)(20,193)(21,192)(22,191)(23,190)(24,189)(25,188)(26,187)(27,186)(28,185)(29,184)(30,183)(31,182)(32,181)(33,180)(34,179)(35,178)(36,177)(37,176)(38,175)(39,174)(40,173)(41,172)(42,171)(43,170)(44,169)(45,168)(46,167)(47,166)(48,165)(49,164)(50,163)(51,162)(52,161)(53,160)(54,159)(55,158)(56,157)(57,156)(58,155)(59,154)(60,153)(61,152)(62,151)(63,150)(64,149)(65,148)(66,147)(67,146)(68,145)(69,144)(70,143)(71,142)(72,141)(73,140)(74,139)(75,138)(76,137)(77,136)(78,135)(79,134)(80,133)(81,132)(82,131)(83,130)(84,129)(85,128)(86,127)(87,126)(88,125)(89,124)(90,123)(91,122)(92,121)(93,120)(94,119)(95,118)(96,117)(97,116)(98,115)(99,114)(100,113)(101,112)(102,111)(103,110)(104,109)(105,108)(106,107)Polycyclic presentation:
2,5,11,179|b^a=b^4,c^a=c^10,d^a=d^1784924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19690, 9);