Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62892 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62948 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6586 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)(16,25)(17,23)(18,29)(19,27)(20,24)(21,28)(22,26)(31,35)(36,42)(37,43)(44,45);(14,16)(15,19)(17,18)(20,27)(21,29)(22,23)(24,25)(26,28);(14,17)(15,21)(16,26)(18,27)(19,22)(20,28)(23,24)(25,29)(30,31)(32,36)(33,37)(34,35)(38,44)(39,42)(40,45)(41,43);(14,18,20,26)(15,22,24,29)(16,17,27,28)(19,23,25,21)(30,32,34,39)(31,36,35,42)(33,40,41,38)(37,45,43,44);(14,17)(15,23)(16,18)(19,22)(20,28)(21,24)(25,29)(26,27)(30,33,34,41)(31,37,35,43)(32,38,39,40)(36,44,42,45);(14,19)(15,16)(17,22)(18,23)(20,25)(21,26)(24,27)(28,29)(30,31)(32,36)(33,37)(34,35)(38,44)(39,42)(40,45)(41,43)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55936);