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×#63070 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6588 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,21,20)(16,22,25,18)(17,26,19,23)(24,28,27,29)(30,31)(32,40)(33,43)(34,37)(35,39)(36,38)(41,42)(44,45);(14,16)(15,22)(17,27)(18,20)(19,24)(21,25)(23,28)(26,29)(30,32,37,36)(31,38,34,40)(33,41,39,44)(35,42,43,45);(14,17,21,19)(15,23,20,26)(16,24,25,27)(18,28,22,29)(30,33)(31,35)(32,41)(34,43)(36,44)(37,39)(38,42)(40,45);(14,18)(15,16)(17,28)(19,29)(20,25)(21,22)(23,24)(26,27)(30,34,37,31)(32,38,36,40)(33,43,39,35)(41,42,44,45);(14,19,21,17)(15,23,20,26)(16,24,25,27)(18,29,22,28)(30,35,37,43)(31,39,34,33)(32,42,36,45)(38,44,40,41);(14,20,21,15)(16,18,25,22)(17,26,19,23)(24,28,27,29)(30,36,37,32)(31,38,34,40)(33,44,39,41)(35,42,43,45)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56058);