Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63041 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#63051 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6720 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)(16,24)(17,19)(18,22)(20,21)(23,27)(25,29)(26,28)(30,31)(32,37)(33,36)(34,38)(35,40)(39,44)(41,42)(43,45);(15,21)(17,27)(22,24)(25,28)(30,31)(32,37)(33,41)(34,38)(35,40)(36,42)(39,43)(44,45);(14,16,20,18)(15,22,21,24)(17,25,27,28)(19,26,23,29)(30,32)(31,35)(33,39)(34,40)(36,43)(37,38)(41,44)(42,45);(14,17)(15,23)(16,25)(18,28)(19,21)(20,27)(22,29)(24,26)(30,33)(31,36)(32,39)(34,42)(35,43)(37,44)(38,41)(40,45);(14,18,20,16)(15,22,21,24)(17,28,27,25)(19,26,23,29)(30,32)(31,37)(33,39)(34,40)(35,38)(36,44)(41,43)(42,45);(14,19,20,23)(15,17,21,27)(16,26,18,29)(22,25,24,28)(30,31)(32,35)(33,36)(34,38)(37,40)(39,43)(41,42)(44,45)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56039);