Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13×C16 · Schur multiplier (H2) = C4 |
| direct product | C13×#13641 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C13×C16 | C23 |
| commutator | C22 | C22×C13×C16 |
| Frattini, cosocle | C2×C16 | C23×C13 |
| socle | C22×C13 | C22×C16 |
| prime radical | C23×C13 | C2×C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C13×C16 ◁ G | |
180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 85 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 85 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23,25,30,26,31,38,48,27,32,39,49,41,51,60,70,28,33,40,50,42,52,61,71,43,53,62,72,63,73,78,83)(24,29,35,45,36,46,57,67,37,47,58,68,59,69,77,82,34,44,54,64,55,65,74,79,56,66,75,80,76,81,84,85);(15,18)(19,21)(22,24)(23,29)(25,35)(26,36)(27,37)(28,34)(30,45)(31,46)(32,47)(33,44)(38,57)(39,58)(40,54)(41,59)(42,55)(43,56)(48,67)(49,68)(50,64)(51,69)(52,65)(53,66)(60,77)(61,74)(62,75)(63,76)(70,82)(71,79)(72,80)(73,81)(78,84)(83,85);(14,16,17,20)(15,19,18,21)(24,34)(29,44)(35,54)(36,55)(37,56)(45,64)(46,65)(47,66)(57,74)(58,75)(59,76)(67,79)(68,80)(69,81)(77,84)(82,85)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6629);