Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62870 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6730 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)(16,20)(17,24)(18,19)(21,25)(22,26)(23,29)(27,28)(30,31,34,35)(32,36,40,38)(33,41,42,37)(39,44,45,43);(16,22)(20,26)(23,28)(27,29)(30,31)(32,38)(33,37)(34,35)(36,40)(39,44)(41,42)(43,45);(15,19)(20,26)(21,24)(27,29)(31,35)(36,38)(37,41)(43,44);(14,15)(16,20)(17,21)(18,19)(22,26)(23,27)(24,25)(28,29)(30,31)(32,36)(33,37)(34,35)(38,40)(39,43)(41,42)(44,45);(14,16)(15,20)(17,23)(18,22)(19,26)(21,27)(24,29)(25,28)(30,32,34,40)(31,36,35,38)(33,39,42,45)(37,43,41,44);(14,17)(15,21)(16,23)(18,25)(19,24)(20,27)(22,28)(26,29)(30,33,34,42)(31,37,35,41)(32,39,40,45)(36,43,38,44)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55858);