Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13×C16 · Schur multiplier (H2) = C23 |
| direct product | C13×#13556 |
| subgroup | G/H | |
|---|---|---|
| center | C13×C16 | C22⋊C4 |
| commutator | C22 | C22×C13×C16 |
| Frattini, cosocle | C2×C16 | C23×C13 |
| socle | C2×C13 | C2×C22⋊C16 |
| prime radical | C2×C13×#41 | C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C13×C16 ◁ C22×C13×C16 ◁ G | |
290 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)(14,15,17,23,18,24,32,45,19,25,33,46,35,47,57,69,20,22,34,41,36,42,58,64,37,43,59,65,60,66,74,76)(16,26,28,44,29,48,52,67,30,49,53,68,54,70,72,77,27,21,31,38,50,39,55,61,51,40,56,62,71,63,73,75);(14,16)(15,21)(17,31)(18,29)(19,30)(20,27)(22,26)(23,44)(24,39)(25,40)(28,34)(32,55)(33,56)(35,54)(36,50)(37,51)(38,41)(42,48)(43,49)(45,67)(46,68)(47,63)(52,58)(53,59)(57,73)(60,71)(61,64)(62,65)(66,70)(69,77)(72,74)(75,76);(16,27)(21,26)(28,31)(29,50)(30,51)(38,44)(39,48)(40,49)(52,55)(53,56)(54,71)(61,67)(62,68)(63,70)(72,73)(75,77)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6544);