Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9369 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9369 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C42 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
390 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)(16,19,23,29)(17,22)(18,21)(20,24,28,25)(26,27)(30,31)(32,40)(33,44,46,37)(34,47)(35,39)(36,42)(38,49)(41,54,57,61)(43,55)(45,52,48,53)(50,56,60,58)(51,59);(14,16)(15,19,21,29)(17,25)(18,23)(20,27,28,22)(24,26)(30,32,34,42,35,43,49,59)(31,36,38,40,39,51,47,55)(33,41,48,58,46,57,45,56)(37,50,53,54,44,60,52,61);(14,16)(15,20)(17,25)(18,23)(19,27)(21,28)(22,29)(24,26)(30,33)(31,37)(32,41)(34,48)(35,46)(36,50)(38,53)(39,44)(40,54)(42,58)(43,57)(45,49)(47,52)(51,60)(55,61)(56,59)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2357);