Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#19776 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,17)(16,22,26,29)(18,27,28,21)(20,24,23,25)(30,31)(32,35)(33,36)(34,38)(37,41)(39,42)(40,44)(43,45);(14,16)(15,20)(17,23)(18,24)(19,26)(21,29)(22,27)(25,28)(30,32,34,40)(31,35,38,44)(33,39,41,45)(36,42,37,43);(14,17,19,15)(16,23,26,20)(18,27,28,21)(22,25,29,24)(31,36)(33,41)(35,42)(37,38)(39,45)(43,44);(16,24)(18,28)(20,29)(21,27)(22,23)(25,26)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12764);