Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#9376 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
430 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22)(17,25,27,20)(18,24)(19,21)(23,26,29,28)(30,31,34,38,35,39,33,37)(32,40,42,36,43,44,41,45);(14,16,22,15,19,24,18,21)(17,23,26,20,27,29,28,25)(30,32)(31,36)(33,42)(34,41)(35,43)(37,44)(38,40)(39,45);(14,17)(15,20)(16,23)(18,28)(19,27)(21,25)(22,26)(24,29)(30,32)(31,36)(33,41)(34,42)(35,43)(37,40)(38,44)(39,45)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2364);