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×#62831 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6528 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)(15,19)(17,24)(20,25)(23,28)(30,31,36,41)(32,42,44,37)(33,40,35,38)(34,39,43,45);(16,22)(20,25)(23,28)(27,29)(30,31)(32,42)(33,38)(34,45)(35,40)(36,41)(37,44)(39,43);(14,15,18,19)(16,20,22,25)(17,21,24,26)(23,27,28,29)(30,32,36,44)(31,37,41,42)(33,43,35,34)(38,45,40,39);(30,33,36,35)(31,38,41,40)(32,43,44,34)(37,45,42,39);(14,16)(15,20)(17,23)(18,22)(19,25)(21,27)(24,28)(26,29)(30,34)(31,39)(32,33)(35,44)(36,43)(37,38)(40,42)(41,45);(14,17)(15,21)(16,23)(18,24)(19,26)(20,27)(22,28)(25,29)(30,35,36,33)(31,40,41,38)(32,34,44,43)(37,39,42,45)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55819);