Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61020 |
| 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 | |
1668 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)(32,36,41,50)(33,38,45,54)(34,37,47,39)(42,49,44,53)(43,51,56,48)(46,52,59,55)(57,61,58,60);(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,29)(27,28)(30,32)(31,36)(33,44)(34,43)(35,41)(37,51)(38,53)(39,48)(40,50)(42,45)(46,58)(47,56)(49,54)(52,60)(55,61)(57,59);(16,23)(19,22)(24,29)(26,28)(31,37)(32,41)(34,47)(36,48)(38,52)(39,40)(42,44)(46,59)(49,60)(50,51)(53,61)(54,55);(15,20)(19,22)(21,27)(26,28)(30,33,35,45)(31,38,40,54)(32,42,41,44)(34,46,47,59)(36,49,50,53)(37,52,39,55)(43,57,56,58)(48,60,51,61);(14,17,18,25)(15,21,20,27)(16,24,23,29)(19,26,22,28)(33,45)(38,54)(42,44)(46,59)(49,53)(52,55)(57,58)(60,61)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54008);