Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12927 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1852 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
378 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)(14,15,19,26,21,27,20,25)(16,28,31,55,32,56,43,50)(17,33,36,49,37,53,35,23)(18,38,40,52,42,51,41,24)(22,39,46,62,47,70,45,30)(29,57,60,75,61,73,59,54)(34,65,68,74,69,48,67,64)(44,58,63,66,72,77,71,76);(14,16,19,31,21,32,20,43)(15,22,26,46,27,47,25,45)(17,29,36,60,37,61,35,59)(18,39,40,62,42,70,41,30)(23,44,33,63,49,72,53,71)(24,50,38,28,52,55,51,56)(34,66,68,77,69,76,67,58)(48,73,64,54,65,57,74,75);(14,17)(15,23)(16,29)(18,34)(19,36)(20,35)(21,37)(22,44)(24,48)(25,53)(26,33)(27,49)(28,54)(30,58)(31,60)(32,61)(38,64)(39,66)(40,68)(41,67)(42,69)(43,59)(45,71)(46,63)(47,72)(50,73)(51,74)(52,65)(55,57)(56,75)(62,77)(70,76)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5915);