Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61918 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#533 ◁ G | |
1660 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,21)(18,22)(19,23)(20,26)(25,29)(27,28)(30,31)(32,40)(33,44)(34,38)(35,48)(36,42)(37,46)(39,47)(41,56)(43,51)(45,53)(49,52)(50,60)(54,58)(55,59)(57,61);(14,16,19,26)(15,20,23,24)(17,25,18,27)(21,28,22,29)(30,32,34,42)(31,36,38,40)(33,41,45,57)(35,43,47,59)(37,50,52,54)(39,51,48,55)(44,61,53,56)(46,58,49,60);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,28,24,29)(30,33,34,45)(31,37,38,52)(32,41,42,57)(35,49,47,46)(36,50,40,54)(39,53,48,44)(43,60,59,58)(51,56,55,61);(14,18,19,17)(15,22,23,21)(16,25,26,27)(20,28,24,29)(32,42)(36,40)(41,57)(43,59)(50,54)(51,55)(56,61)(58,60);(15,23)(20,24)(21,22)(28,29)(31,38)(32,42)(37,52)(39,48)(41,57)(43,59)(44,53)(58,60)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54906);