Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13387 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3058 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
428 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16)(18,19)(20,24)(21,25)(22,37)(23,28)(26,34)(27,35)(29,39)(30,47)(31,40)(32,41)(33,42)(36,44)(38,46)(43,49)(45,48);(14,15)(16,17)(18,20)(19,24)(21,33)(22,29)(23,32)(25,42)(26,45)(27,40)(28,41)(30,36)(31,35)(34,48)(37,39)(38,43)(44,47)(46,49);(14,16,17,15)(19,25)(20,29)(21,34)(22,35)(24,38)(26,27)(28,44)(30,33)(31,32)(36,49)(37,43)(39,47)(40,42)(41,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6375);