Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10149 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C2×C13×#127 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
528 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)(16,24)(17,20)(18,22)(19,23)(21,25)(26,28)(27,29)(32,38)(33,40)(35,43)(36,41)(39,42)(44,45);(15,20)(16,25)(17,18)(22,23)(24,28)(26,27)(30,31,34,37)(32,35,39,44)(33,41,40,36)(38,45,42,43);(14,16,19,26)(15,21,23,29)(17,25,18,27)(20,28,22,24)(30,32)(31,35)(33,42)(34,39)(36,45)(37,44)(38,40)(41,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3137);