Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,20)(16,21,17,19)(22,23)(24,28)(25,29)(26,31)(27,33)(30,38)(32,39)(34,47)(35,44)(36,42)(37,43)(40,46)(41,48)(45,51)(49,53)(50,52);(14,16,18,17)(15,19,20,21)(22,24)(23,28)(25,35)(26,34)(27,37)(29,44)(30,41)(31,47)(32,42)(33,43)(36,39)(38,48)(40,49)(45,52)(46,53)(50,51);(14,17,18,16)(15,19,20,21)(23,29)(24,34)(25,38)(26,39)(28,41)(30,32)(31,45)(33,46)(35,49)(36,37)(40,51)(42,53)(43,52)(44,47)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6443);