Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12942 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1862 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
380 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)(14,15,20,27,22,28,21,43)(16,29,33,47,34,60,44,56)(17,35,38,52,39,72,45,71)(18,26,41,57,42,58,19,25)(23,40,48,68,50,32,49,31)(24,51,53,73,55,36,54,37)(30,61,64,46,66,75,65,76)(59,69,77,67,74,62,70,63);(14,16,20,33,22,34,21,44)(15,23,27,48,28,50,43,49)(17,30,38,64,39,66,45,65)(18,40,41,68,42,32,19,31)(24,46,53,75,55,76,54,61)(25,56,26,29,57,47,58,60)(35,70,52,59,72,77,71,74)(36,67,37,62,51,63,73,69);(14,17)(15,24)(16,30)(18,37)(19,36)(20,38)(21,45)(22,39)(23,46)(25,35)(26,52)(27,53)(28,55)(29,59)(31,67)(32,69)(33,64)(34,66)(40,62)(41,51)(42,73)(43,54)(44,65)(47,77)(48,75)(49,61)(50,76)(56,70)(57,72)(58,71)(60,74)(63,68)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5930);