Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33469 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33470 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#442 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
632 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,27,31,57)(17,33)(18,23)(19,40)(20,26)(21,30,46,65)(22,36)(24,38)(25,39)(28,58,61,77)(29,56,32,51)(34,48)(35,52)(37,49)(41,54,66,45)(42,47)(43,50)(44,70,75,73)(53,63)(55,62,74,59)(60,76,64,67)(68,71)(69,72);(14,16)(15,21)(17,28)(18,29)(19,41)(20,31)(22,44)(23,45)(24,51)(25,54)(26,46)(27,50)(30,63)(32,39)(33,67)(34,59)(35,70)(36,62)(37,61)(38,65)(40,57)(42,73)(43,66)(47,58)(48,75)(49,76)(52,77)(53,56)(55,68)(60,69)(64,71)(72,74);(14,17,18,36,20,37,39,34)(15,22,25,33,26,48,23,49)(16,28,29,62,31,61,32,59)(19,42,38,69,43,35,63,71)(21,44,54,67,46,75,45,76)(24,52,40,72,53,47,50,68)(27,55,51,77,57,74,56,58)(30,64,41,73,65,60,66,70);(14,18,20,39)(15,23,26,25)(16,29,31,32)(17,34,37,36)(19,38,43,63)(21,45,46,54)(22,33,48,49)(24,50,53,40)(27,56,57,51)(28,59,61,62)(30,41,65,66)(35,69,42,71)(44,67,75,76)(47,68,52,72)(55,77,74,58)(60,73,64,70)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26458);