Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#12902 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C13 | #127 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1843 |
| prime radical | C23×C13 | #131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C13 ◁ C22×C8×C13 ◁ G | |
278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,23,19,24,34,45,20,25,35,46,36,47,60,71)(16,21,28,39,29,40,53,65,27,38,51,63,52,64,73,76)(17,22,32,43,33,44,59,70,31,42,57,68,58,69,75,77)(26,48,50,72,30,54,56,74,49,37,61,62,55,41,66,67);(14,16)(15,21)(17,30,31,55)(18,28)(19,29)(20,27)(22,41,42,54)(23,39)(24,40)(25,38)(26,33,49,58)(32,56,57,66)(34,53)(35,51)(36,52)(37,44,48,69)(43,67,68,74)(45,65)(46,63)(47,64)(50,59,61,75)(60,73)(62,70,72,77)(71,76);(14,17)(15,22)(16,26,27,49)(18,32)(19,33)(20,31)(21,37,38,48)(23,43)(24,44)(25,42)(28,50,51,61)(29,30,52,55)(34,59)(35,57)(36,58)(39,62,63,72)(40,41,64,54)(45,70)(46,68)(47,69)(53,56,73,66)(60,75)(65,67,76,74)(71,77)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5890);