Finite Group DatabasebetaFinite Group Databasebeta| order | 20068 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C29×C173 ⋊ C4 |
| Sylow | C173 ⋊ #1181 |
| Sylow | C29 ⋊ #10621924 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C173 | C4 |
| prime radical, cosocle | D5017 | C2 |
| LCS | G ▷ C29×C173 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 202 |
| transitive degree | μt(G) = 5017 |
A minimal faithful permutation representation — 2 generators on 202 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)(70,93,94,118)(74,97,98,115)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,95,113,100)(92,116,117,96)(99,119,120,137)(103,122,123,136)(107,126,127,133)(111,130,131,129)(114,121,134,125)(124,138,139,152)(128,141,142,151)(132,145,146,148)(135,140,149,144)(143,153,154,163)(147,156,157,162)(150,155,160,159)(158,164,165,170)(161,166,167,169)(168,171,172,173)(175,176,177,179)(178,181,182,188)(180,185,186,184)(183,190,191,199)(187,192,194,196)(189,197,198,193)(195,200,201,202);(1,2,5,10,19,32,49,70,95,84,59,38,21,8,16,27,40,57,78,103,124,140,130,105,76,51,30,46,65,86,111,132,147,158,166,156,141,122,97,68,92,118,137,152,163,170,173,172,167,160,149,134,113,89,66,87,112,133,148,159,154,142,127,106,81,60,43,28,41,58,79,104,125,120,98,73,52,35,22,13,6,11,20,33,50,71,96,116,88,63,42,25,12,3,7,14,23,36,53,74,99,121,109,80,55,34,17,29,44,61,82,107,128,143,155,145,126,101,72,47,67,90,114,135,150,161,168,171,164,153,138,119,93,117,91,115,136,151,162,169,165,157,146,131,110,85,64,45,62,83,108,129,144,139,123,102,77,56,39,26,15,24,37,54,75,100,94,69,48,31,18,9,4)(174,175,178,183,192,181,189,199,202,201,194,186,179,184,193,197,185,176,180,187,195,200,190,198,188,196,191,182,177)Polycyclic presentation:
2^2,29,173|a^2=b,c^a=c^17,d^a=d^93,c^b=c^28,d^b=d^1721258 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20068, 8);