Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8491 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#8502 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #379 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#3547 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,23,25,19)(17,22)(18,21)(20,24,28,26)(27,29)(30,31,35,40,36,41,34,39)(32,42,46,37,45,52,44,51)(33,38,47,53,48,54,49,55)(43,57,58,61,59,56,60,50);(14,16)(15,19)(17,24)(18,25)(20,22)(21,23)(26,27)(28,29)(30,32)(31,37)(33,43)(34,46)(35,44)(36,45)(38,50)(39,52)(40,42)(41,51)(47,60)(48,59)(49,58)(53,56)(54,61)(55,57);(14,16)(15,20)(17,26)(18,25)(19,22)(21,28)(23,29)(24,27)(30,33,36,48)(31,38,41,54)(32,43,45,59)(34,49,35,47)(37,50,51,61)(39,55,40,53)(42,56,52,57)(44,60,46,58)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1490);