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×#62827 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6626 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)(16,23)(17,18)(19,20)(21,26)(22,27)(24,29)(25,28)(31,35)(33,40)(36,41)(39,44);(15,20)(17,22)(21,23)(24,28)(32,38)(36,41)(39,44)(43,45);(14,15,19,20)(16,21,26,23)(17,18,22,27)(24,25,28,29)(30,31,34,35)(32,36,38,41)(33,37,40,42)(39,43,44,45);(14,16,19,26)(15,21,20,23)(17,24,22,28)(18,25,27,29);(14,17,19,22)(15,18,20,27)(16,24,26,28)(21,25,23,29)(30,32)(31,36)(33,39)(34,38)(35,41)(37,43)(40,44)(42,45);(14,18)(15,22)(16,25)(17,20)(19,27)(21,28)(23,24)(26,29)(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, 55815);