Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33854 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33855 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C13×#443 ◁ G | |
640 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)(14,15,21,27)(16,28,33,61)(17,34,37,57)(18,38,43,55)(19,26,20,25)(22,46,50,31)(23,44,52,36)(24,41,56,42)(29,62,66,48)(30,67,70,47)(32,71,45,53)(35,73,68,51)(39,58,74,49)(40,54,75,77)(59,65,76,64)(60,63,72,69);(14,16,21,33)(15,22,27,50)(17,29,37,66)(18,39,43,74)(19,32,20,45)(23,47,52,67)(24,53,56,71)(25,49,26,58)(28,55,61,38)(30,68,70,35)(31,41,46,42)(34,72,57,60)(36,64,44,65)(40,63,75,69)(48,73,62,51)(54,59,77,76);(14,17)(15,23)(16,29)(18,35)(19,44)(20,36)(21,37)(22,47)(24,51)(25,57)(26,34)(27,52)(28,59)(30,39)(31,63)(32,65)(33,66)(38,54)(40,42)(41,75)(43,68)(45,64)(46,69)(48,53)(49,60)(50,67)(55,77)(56,73)(58,72)(61,76)(62,71)(70,74);(14,17)(15,23)(16,30)(18,40)(19,36)(20,44)(21,37)(22,48)(24,54)(25,34)(26,57)(27,52)(28,60)(29,39)(31,65)(32,63)(33,70)(35,42)(38,51)(41,68)(43,75)(45,69)(46,64)(47,53)(49,59)(50,62)(55,73)(56,77)(58,76)(61,72)(66,74)(67,71)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26843);