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×#61018 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#535 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×C13×#41 ◁ G | |
1672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
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)(32,37)(33,43)(34,39)(35,49)(36,40)(38,41)(42,51)(44,53)(45,57)(46,50)(47,54)(48,55)(52,56)(58,61)(59,60);(14,16)(15,19)(17,24)(18,23)(20,22)(21,26)(25,29)(27,28)(30,32,36,35)(31,37,40,49)(33,44,46,41)(34,47,48,42)(38,43,53,50)(39,54,55,51)(45,56,59,58)(52,60,61,57);(16,23)(19,22)(24,29)(26,28)(30,33,36,46)(31,38,40,53)(32,41,35,44)(34,45,48,59)(37,50,49,43)(39,52,55,61)(42,56,47,58)(51,60,54,57);(15,20)(19,22)(21,27)(26,28)(30,34)(31,39)(32,42)(33,45)(35,47)(36,48)(37,51)(38,52)(40,55)(41,56)(43,57)(44,58)(46,59)(49,54)(50,60)(53,61);(14,17,18,25)(15,21,20,27)(16,24,23,29)(19,26,22,28)(34,48)(39,55)(42,47)(45,59)(51,54)(52,61)(56,58)(57,60)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54006);