Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9431 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9431 |
| 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 | |
414 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)(15,19)(16,22)(17,25)(21,27)(23,24)(26,28)(30,31)(32,39,40,43)(33,36,41,42)(34,37)(35,38)(44,45);(14,15,17,19,18,21,25,27)(16,20,23,26,24,29,22,28)(30,32,34,42,35,40,44,36)(31,33,37,43,38,41,45,39);(14,16)(15,20)(17,23)(18,24)(19,26)(21,29)(22,25)(27,28)(30,33)(31,36)(32,37)(34,43)(35,41)(38,42)(39,44)(40,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2419);