Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#60882 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3512 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1650 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22)(17,20)(18,21)(19,24)(23,28)(25,27)(26,29)(30,31)(32,37)(33,39)(34,40)(35,49)(36,41)(38,46)(42,51)(43,52)(44,59)(45,53)(47,54)(48,55)(50,56)(57,60)(58,61);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32,36,45)(31,37,41,53)(33,42,47,57)(34,43,35,44)(38,50,55,61)(39,51,54,60)(40,52,49,59)(46,56,48,58);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(30,33)(31,38)(32,42)(34,46)(35,48)(36,47)(37,50)(39,49)(40,54)(41,55)(43,56)(44,58)(45,57)(51,59)(52,60)(53,61);(15,21)(19,22)(20,29)(27,28)(30,33)(31,39)(32,42)(34,48)(35,46)(36,47)(37,51)(38,49)(40,55)(41,54)(43,58)(44,56)(45,57)(50,59)(52,61)(53,60);(30,34,36,35)(31,40,41,49)(32,43,45,44)(33,46,47,48)(37,52,53,59)(38,54,55,39)(42,56,57,58)(50,60,61,51)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53870);