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×#62945 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6478 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)(14,15,19,23)(16,24,27,20)(17,28,26,21)(18,22,25,29)(31,35)(36,42)(37,43)(44,45);(14,16)(15,20)(17,25)(18,26)(19,27)(21,29)(22,28)(23,24);(14,17)(15,21)(16,18)(19,26)(20,22)(23,28)(24,29)(25,27)(30,31)(32,36)(33,37)(34,35)(38,44)(39,42)(40,45)(41,43);(14,17)(15,21)(16,25)(18,27)(19,26)(20,29)(22,24)(23,28)(30,32,34,39)(31,36,35,42)(33,40,41,38)(37,45,43,44);(14,18,19,25)(15,22,23,29)(16,26,27,17)(20,28,24,21)(30,33,34,41)(31,37,35,43)(32,38,39,40)(36,44,42,45);(14,15)(16,20)(17,21)(18,22)(19,23)(24,27)(25,29)(26,28)(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, 55933);