Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61946 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3221 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#533 ◁ G | |
1646 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)(32,42)(33,46)(34,41)(35,39)(36,40)(37,45)(38,47)(43,57)(44,52)(48,55)(49,54)(50,53)(51,58)(56,60)(59,61);(14,16,19,26)(15,20,23,24)(17,25,18,27)(21,28,22,29)(30,32)(31,37)(33,43)(34,49)(35,45)(36,44)(38,51)(39,42)(40,54)(41,52)(46,61)(47,60)(48,59)(50,58)(53,56)(55,57);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,28,24,29)(30,33,35,48)(31,38,39,53)(32,43,45,59)(34,47,36,50)(37,51,42,56)(40,46,41,55)(44,58,49,60)(52,57,54,61);(14,18,19,17)(15,22,23,21)(16,25,26,27)(20,28,24,29)(31,39)(37,42)(38,53)(40,41)(46,55)(51,56)(52,54)(57,61);(15,23)(20,24)(21,22)(28,29)(30,34,35,36)(31,40,39,41)(32,44,45,49)(33,47,48,50)(37,52,42,54)(38,46,53,55)(43,58,59,60)(51,57,56,61)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54934);