Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36838 |
| 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 | |
1526 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)(24,28)(27,29)(30,31)(32,38)(33,39)(34,37)(35,36)(40,44)(41,45)(42,43);(15,18)(19,21)(22,23,26,25)(24,27,28,29)(31,36)(32,39)(37,43)(40,45);(14,15)(16,19)(17,18)(20,21)(22,24,26,28)(23,27,25,29)(30,32)(31,33)(34,40)(35,39)(36,38)(37,41)(42,45)(43,44);(14,15)(16,19)(17,18)(20,21)(22,25,26,23)(24,29,28,27)(30,33)(31,32)(34,41)(35,38)(36,39)(37,40)(42,44)(43,45);(14,16)(15,19)(17,20)(18,21)(30,34,35,42)(31,37,36,43)(32,40,39,45)(33,41,38,44)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29826);