Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62817 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62828 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6636 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,18)(17,25)(19,20)(21,23)(22,27)(24,28)(26,29)(31,35)(33,40)(36,41)(39,44);(15,20)(16,23)(22,25)(24,29)(32,38)(36,41)(39,44)(43,45);(14,16,19,23)(15,21,20,18)(17,24,27,29)(22,28,25,26)(30,31,34,35)(32,36,38,41)(33,37,40,42)(39,43,44,45);(14,17)(15,22)(16,24)(18,26)(19,27)(20,25)(21,28)(23,29);(14,15)(16,21)(17,22)(18,23)(19,20)(24,28)(25,27)(26,29)(30,32)(31,36)(33,39)(34,38)(35,41)(37,43)(40,44)(42,45);(14,18,19,21)(15,23,20,16)(17,26,27,28)(22,29,25,24)(30,33)(31,37)(32,39)(34,40)(35,42)(36,43)(38,44)(41,45)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55816);