Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61922 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#449 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#533 ◁ G | |
1640 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)(16,24)(17,21)(18,22)(19,23)(20,26)(25,29)(27,28)(30,31)(32,37)(33,44)(34,39)(35,48)(36,40)(38,45)(41,56)(42,51)(43,53)(46,54)(47,52)(49,55)(50,58)(57,60)(59,61);(14,16,19,26)(15,20,23,24)(17,25,18,27)(21,28,22,29)(30,32,36,43)(31,37,40,53)(33,41,46,59)(34,47,35,42)(38,50,55,60)(39,52,48,51)(44,56,54,61)(45,58,49,57);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,28,24,29)(30,33)(31,38)(32,41)(34,45)(35,49)(36,46)(37,50)(39,54)(40,55)(42,57)(43,59)(44,48)(47,58)(51,56)(52,61)(53,60);(14,18,19,17)(15,22,23,21)(16,25,26,27)(20,28,24,29);(15,23)(20,24)(21,22)(28,29)(30,34,36,35)(31,39,40,48)(32,42,43,47)(33,45,46,49)(37,51,53,52)(38,54,55,44)(41,57,59,58)(50,56,60,61)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54910);