Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18722 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3549 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
1004 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)(14,15)(16,21)(17,23)(18,22)(19,24)(20,25)(26,29)(27,28)(30,31,35,39)(32,40,43,44)(33,38,34,37)(36,41,45,42);(14,16)(15,20)(17,25)(18,27)(19,26)(21,22)(23,29)(24,28)(30,32)(31,36)(33,41)(34,42)(35,43)(37,44)(38,40)(39,45);(14,16)(15,21)(17,27)(18,25)(19,26)(20,22)(23,28)(24,29)(31,37)(33,34)(36,44)(38,39)(40,45)(41,42);(14,17,19,18)(15,22,24,23)(16,25,26,27)(20,21,28,29)(30,33,35,34)(31,37,39,38)(32,41,43,42)(36,44,45,40)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11710);