Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18235 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
938 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)(14,15,18,21)(16,19,23,26)(17,20,24,27)(22,28,29,25)(31,35)(33,40)(36,44)(37,41)(39,42)(43,45);(14,16)(15,19)(17,22)(18,23)(20,25)(21,26)(24,29)(27,28)(30,31,34,37)(32,36,38,45)(33,41,40,35)(39,43,42,44);(14,17)(15,20)(16,22)(18,24)(19,25)(21,27)(23,29)(26,28)(30,32)(31,36)(33,42)(34,38)(35,43)(37,45)(39,40)(41,44);(32,38)(36,45)(39,42)(43,44)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11223);