Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C101 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | #87938 |
| commutator, hypocenter | C101 | C128 |
| Fitting | C32×C101 | C4 |
| socle, prime radical | C2×C101 | C64 |
| cosocle | #20264896 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C32 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 229 |
| transitive degree | μt(G) = 12928 |
A minimal faithful permutation representation — 2 generators on 229 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)(32,47,48,65)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,49,63,50)(53,66,67,80)(57,70,71,77)(61,74,75,73)(64,68,78,69)(72,81,82,91)(76,85,86,88)(79,83,89,84)(87,92,93,98)(90,94,96,95)(97,99,100,101)(102,103,104,110,105,111,116,131,106,112,117,132,121,136,146,166,107,113,118,133,122,137,147,167,125,140,150,170,156,176,186,201,108,114,119,134,123,138,148,168,126,141,151,171,157,177,187,202,128,143,153,173,159,179,189,204,162,182,192,207,196,211,216,222,109,115,120,135,124,139,149,169,127,142,152,172,158,178,188,203,129,144,154,174,160,180,190,205,163,183,193,208,197,212,217,223,130,145,155,175,161,181,191,206,164,184,194,209,198,213,218,224,165,185,195,210,199,214,219,225,200,215,220,226,221,227,228,229);(1,2,5,10,19,32,49,42,25,12,3,7,14,23,36,53,68,59,38,21,8,16,27,40,57,72,83,74,55,34,17,29,44,61,76,87,94,85,70,51,30,46,64,79,90,97,99,92,81,66,47,65,80,91,98,101,100,96,89,78,63,45,62,77,88,95,93,86,75,60,43,28,41,58,73,84,82,71,56,39,26,15,24,37,54,69,67,52,35,22,13,6,11,20,33,50,48,31,18,9,4)Polycyclic presentation:
2^7,101|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^10,h^b=h^100928 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 19325);