Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12841 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #466 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1808 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ 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)(16,27)(17,34,37,48)(18,38)(19,25)(20,42)(21,26)(22,30)(23,36,47,41)(24,28)(29,56,59,75)(31,52)(32,63)(33,53)(35,46,66,73)(39,49)(40,68)(43,70,71,77)(44,60)(45,61)(50,58,74,62)(51,54)(55,65,69,67)(57,64,76,72);(14,16,28,54,20,32,40,61,21,33,39,60,19,31,18,30)(15,22,38,52,25,44,49,53,26,45,68,63,42,51,24,27)(17,29,55,70,36,58,66,76,37,59,69,77,41,62,35,57)(23,43,67,75,48,72,73,74,47,71,65,56,34,64,46,50);(14,17)(15,23)(16,29)(18,35)(19,41)(20,36)(21,37)(22,43)(24,46)(25,48)(26,47)(27,50)(28,55)(30,57)(31,62)(32,58)(33,59)(34,42)(38,67)(39,69)(40,66)(44,72)(45,71)(49,73)(51,64)(52,75)(53,74)(54,70)(56,63)(60,77)(61,76)(65,68)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5829);