Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #63091 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C214 |
| direct product | C13×#63093 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C24×D4 |
| commutator, Frattini, cosocle | C4 | C26×C13 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C13×#585 ◁ G | |
10698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,20,25)(16,26,30,47)(17,22,32,43)(18,23,34,45)(19,36,38,24)(21,37,41,29)(27,48,51,68)(28,49,53,69)(31,42,55,66)(33,58,57,44)(35,61,60,46)(39,59,64,52)(40,62,65,54)(50,70,71,77)(56,74,73,67)(63,75,76,72);(14,16,20,30)(15,21,25,41)(17,27,32,51)(18,28,34,53)(19,37,38,29)(22,39,43,64)(23,40,45,65)(24,47,36,26)(31,50,55,71)(33,59,57,52)(35,62,60,54)(42,63,66,76)(44,68,58,48)(46,69,61,49)(56,75,73,72)(67,77,74,70);(14,17)(15,22)(16,27)(18,31)(19,33)(20,32)(21,39)(23,42)(24,44)(25,43)(26,48)(28,50)(29,52)(30,51)(34,55)(35,56)(36,58)(37,59)(38,57)(40,63)(41,64)(45,66)(46,67)(47,68)(49,70)(53,71)(54,72)(60,73)(61,74)(62,75)(65,76)(69,77);(14,18)(15,23)(16,28)(17,31)(19,35)(20,34)(21,40)(22,42)(24,46)(25,45)(26,49)(27,50)(29,54)(30,53)(32,55)(33,56)(36,61)(37,62)(38,60)(39,63)(41,65)(43,66)(44,67)(47,69)(48,70)(51,71)(52,72)(57,73)(58,74)(59,75)(64,76)(68,77);(18,34)(23,45)(28,53)(31,55)(35,60)(40,65)(42,66)(46,61)(49,69)(50,71)(54,62)(56,73)(63,76)(67,74)(70,77)(72,75);(17,32)(22,43)(27,51)(31,55)(33,57)(39,64)(42,66)(44,58)(48,68)(50,71)(52,59)(56,73)(63,76)(67,74)(70,77)(72,75)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56081);