Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12026 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12832 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #427 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1807 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C13×M16 ◁ C2×C13×#131 ◁ G | |
358 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)(16,26,29,47)(17,31,33,22)(18,35)(19,38)(20,24)(21,28,41,53)(23,36)(25,39)(27,49)(30,56,55,48)(32,60,61,64)(34,44,63,59)(37,65)(40,50)(42,69,67,54)(43,62,58,76)(45,66)(46,52)(51,70)(57,74)(68,77)(71,73)(72,75);(14,16,18,28,19,30,36,54,20,29,37,53,39,55,66,69)(15,21,23,26,25,42,35,48,24,41,45,47,38,67,65,56)(17,27,32,50,34,51,62,73,33,52,61,74,63,75,76,77)(22,40,43,46,44,68,64,70,31,57,58,49,59,71,60,72);(14,17)(15,22)(16,27)(18,32)(19,34)(20,33)(21,40)(23,43)(24,31)(25,44)(26,46)(28,50)(29,52)(30,51)(35,64)(36,62)(37,61)(38,59)(39,63)(41,57)(42,68)(45,58)(47,49)(48,70)(53,74)(54,73)(55,75)(56,72)(60,65)(66,76)(67,71)(69,77)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5820);