Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61386 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#533 ◁ G | |
1690 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,17)(16,20,21,19)(22,23,26,30)(24,32,34,28)(25,36,37,45)(27,40,39,31)(29,41,44,38)(33,48,49,53)(35,43,51,47)(42,50,46,52);(14,16,18,21)(15,19,17,20)(22,24,26,34)(23,28,30,32)(25,33,37,49)(27,35,39,51)(29,42,44,46)(31,43,40,47)(36,53,45,48)(38,50,41,52);(22,25,26,37)(23,29,30,44)(24,33,34,49)(27,41,39,38)(28,42,32,46)(31,45,40,36)(35,52,51,50)(43,48,47,53);(14,17,18,15)(16,19,21,20)(24,34)(28,32)(33,49)(35,51)(42,46)(43,47)(48,53)(50,52);(23,30)(24,34)(29,44)(31,40)(33,49)(35,51)(36,45)(50,52)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54374);