Finite Group DatabasebetaFinite Group Databasebeta| order | 13396 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C17×C197 ⋊ C4 |
| Sylow | C197 ⋊ Dic17 |
| Sylow | C17 ⋊ #11716161 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C197 | C4 |
| prime radical, cosocle | C17×D197 | C2 |
| LCS | G ▷ C17×C197 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 214 |
| transitive degree | μt(G) = 3349 |
A minimal faithful permutation representation — 2 generators on 214 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)(74,97,95,114)(78,99,100,110)(82,103,104,106)(86,107,108,102)(90,111,112,98)(92,115,116,96)(101,122,123,137)(105,126,127,133)(109,130,131,129)(113,134,135,125)(117,138,139,121)(119,124,141,120)(128,145,146,156)(132,149,150,152)(136,153,154,148)(140,157,158,144)(142,147,160,143)(151,164,165,171)(155,168,169,167)(159,172,173,163)(161,166,175,162)(170,179,180,182)(174,183,184,178)(176,181,186,177)(185,190,191,189)(187,192,193,188)(194,196,197,195)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214);(1,2,5,10,19,32,49,70,95,73,52,35,22,13,6,11,20,33,50,71,96,120,123,100,77,56,39,26,15,24,37,54,75,98,121,143,146,127,104,81,60,43,28,41,58,79,102,125,144,162,165,150,131,108,85,64,45,62,83,106,129,148,163,177,180,169,154,135,112,89,66,87,110,133,152,167,178,188,191,184,173,158,139,116,91,114,137,156,171,182,189,195,197,193,186,175,160,141,118,93,119,142,161,176,187,194,196,190,179,164,145,122,97,68,92,117,140,159,174,185,192,183,168,149,126,99,72,47,67,90,113,136,155,170,181,172,153,130,103,76,51,30,46,65,86,109,132,151,166,157,134,107,80,55,34,17,29,44,61,82,105,128,147,138,111,84,59,38,21,8,16,27,40,57,78,101,124,115,88,63,42,25,12,3,7,14,23,36,53,74,94,69,48,31,18,9,4)(198,199,201,203,205,207,209,211,213,214,212,210,208,206,204,202,200)Polycyclic presentation:
2^2,17,197|a^2=b,c^a=c^16,d^a=d^183,d^b=d^196853 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13396, 11);