Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,20)(18,21)(22,28)(23,26)(24,27)(25,29)(30,31,36,41)(32,42,45,55)(33,38,47,53)(34,40,35,39)(37,49,51,44)(43,56,59,60)(46,54,48,52)(50,57,61,58);(14,16)(15,19)(17,22)(18,23)(20,25)(21,26)(24,29)(27,28)(30,32)(31,37)(33,43)(34,44)(35,49)(36,45)(38,50)(39,42)(40,55)(41,51)(46,57)(47,59)(48,58)(52,60)(53,61)(54,56);(14,17)(15,20)(16,22)(18,24)(19,25)(21,27)(23,29)(26,28)(30,33,36,47)(31,38,41,53)(32,43,45,59)(34,48,35,46)(37,50,51,61)(39,54,40,52)(42,56,55,60)(44,58,49,57);(15,21)(19,26)(20,27)(25,28)(30,34,36,35)(31,39,41,40)(32,44,45,49)(33,46,47,48)(37,42,51,55)(38,52,53,54)(43,57,59,58)(50,60,61,56)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11443);