Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62743 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| socle | C22×C13 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ G | |
6634 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)(16,22)(17,21)(18,20)(19,23)(24,28)(25,27)(26,29)(30,31)(32,35)(33,40)(34,37)(36,41)(38,44)(39,43)(42,45);(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,29)(27,28)(30,32)(31,35)(33,38)(34,39)(36,42)(37,43)(40,44)(41,45);(16,23)(19,22)(24,29)(26,28)(30,33,34,41)(31,36,37,40)(32,38,39,45)(35,42,43,44);(15,20)(19,22)(21,27)(26,28)(32,39)(35,43)(38,45)(42,44);(31,37)(35,43)(36,40)(42,44);(14,17,18,25)(15,21,20,27)(16,24,23,29)(19,26,22,28)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55731);