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×#61013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1656 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)(17,21)(18,20)(19,23)(24,28)(25,27)(26,29)(30,31,35,40)(32,41,36,37)(33,44,47,52)(34,48,50,39)(38,45,54,42)(43,51,49,55)(46,59,60,57)(53,56,61,58);(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,29)(27,28)(30,32,35,36)(31,37,40,41)(33,45,47,42)(34,49,50,43)(38,52,54,44)(39,55,48,51)(46,56,60,58)(53,57,61,59);(16,23)(19,22)(24,29)(26,28)(30,33,35,47)(31,38,40,54)(32,42,36,45)(34,46,50,60)(37,44,41,52)(39,53,48,61)(43,56,49,58)(51,57,55,59);(15,20)(19,22)(21,27)(26,28)(30,34)(31,39)(32,43)(33,46)(35,50)(36,49)(37,51)(38,53)(40,48)(41,55)(42,56)(44,57)(45,58)(47,60)(52,59)(54,61);(14,17,18,25)(15,21,20,27)(16,24,23,29)(19,26,22,28)(34,50)(39,48)(43,49)(46,60)(51,55)(53,61)(56,58)(57,59)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54001);