Finite Group DatabasebetaFinite Group Databasebeta| order | 12879 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C53 · Schur multiplier (H2) = C9 |
| direct product | C53×#6898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C53 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C53 |
| prime radical | C33×C53 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C53 ◁ G | |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 107 |
| transitive degree | μt(G) = 4293 |
A minimal faithful permutation representation — 3 generators on 107 points:
(1,2,5)(3,6,12)(4,8,13)(7,17,11)(9,14,20)(10,16,21)(15,24,19)(18,23,26)(22,27,25)(28,29,32)(30,34,40)(31,35,39)(33,41,38)(36,43,48)(37,44,47)(42,49,46)(45,51,53)(50,54,52)(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);(1,3,9,4,10,18,11,19,25)(2,6,14,8,16,23,7,15,22)(5,12,20,13,21,26,17,24,27)(29,33,35)(32,39,41)(34,42,44)(40,47,49)(43,50,51)(48,53,54);(2,7,8)(5,13,17)(6,15,16)(12,21,24)(14,22,23)(20,26,27)(28,30,36,38,46,52,31,37,45)(29,34,43,33,42,50,35,44,51)(32,40,48,41,49,54,39,47,53)2703 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12879, 45);