Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C157 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | #10597845 |
| commutator, hypocenter | C157 | C128 |
| Fitting | C32×C157 | C4 |
| socle, prime radical | C2×C157 | C64 |
| cosocle | #23756992 | C2 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C32 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 285 |
| transitive degree | μt(G) = 20096 |
A minimal faithful permutation representation — 2 generators on 285 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,146)(99,126,127,142)(103,130,131,140)(107,134,135,138)(111,137,132,136)(115,139,128,133)(119,141,124,129)(121,143,144,125)(145,150,151,149)(147,152,153,148)(154,156,157,155)(158,159,160,166,161,167,172,187,162,168,173,188,177,192,202,222,163,169,174,189,178,193,203,223,181,196,206,226,212,232,242,257,164,170,175,190,179,194,204,224,182,197,207,227,213,233,243,258,184,199,209,229,215,235,245,260,218,238,248,263,252,267,272,278,165,171,176,191,180,195,205,225,183,198,208,228,214,234,244,259,185,200,210,230,216,236,246,261,219,239,249,264,253,268,273,279,186,201,211,231,217,237,247,262,220,240,250,265,254,269,274,280,221,241,251,266,255,270,275,281,256,271,276,282,277,283,284,285);(1,2,5,10,19,32,49,70,95,124,118,91,116,140,134,101,72,47,67,90,115,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,148,151,144,120,142,137,105,76,51,30,46,65,86,111,131,102,77,56,39,26,15,24,37,54,75,100,129,149,155,157,153,146,139,109,80,55,34,17,29,44,61,82,107,135,106,81,60,43,28,41,58,79,104,133,122,147,154,156,150,141,113,84,59,38,21,8,16,27,40,57,78,103,132,110,85,64,45,62,83,108,136,126,93,121,145,152,143,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,114,89,66,87,112,138,130,97,68,92,119,123,94,69,48,31,18,9,4)Polycyclic presentation:
2^7,157|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^129,h^b=h^1561376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 19325);