Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36861 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(16,20)(19,21)(23,26)(27,29)(31,32)(33,40)(34,42)(43,44);(15,18)(19,21)(30,31,35,32)(33,38,40,36)(34,37,42,39)(41,44,45,43);(14,15)(16,19)(17,18)(20,21)(22,23)(24,27)(25,26)(28,29)(30,32,35,31)(33,38,40,36)(34,39,42,37)(41,44,45,43);(14,15)(16,19)(17,18)(20,21)(30,33)(31,36)(32,38)(34,41)(35,40)(37,43)(39,44)(42,45);(14,16)(15,19)(17,20)(18,21)(22,24,25,28)(23,27,26,29)(30,34)(31,37)(32,39)(33,41)(35,42)(36,43)(38,44)(40,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29849);