Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19028 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3217 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
888 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(16,23)(17,18)(22,25)(24,26)(27,29)(31,35)(33,40)(36,44)(37,41)(38,42)(43,45);(14,15)(16,21)(17,25)(18,20)(19,22)(23,29)(24,28)(26,27)(30,31,34,37)(32,36,39,45)(33,41,40,35)(38,43,42,44);(14,16,19,24)(15,21,22,28)(17,23,18,26)(20,27,25,29)(30,32,34,39)(31,36,37,45)(33,42,40,38)(35,43,41,44);(15,22)(20,25)(21,28)(27,29)(31,37)(35,41)(36,45)(43,44)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12016);