Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34526 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1800 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19)(20,26)(21,23)(22,29)(24,27)(25,30)(28,31)(32,33)(34,35,38,41)(36,42,44,39)(37,40,45,47)(43,48,49,46);(19,21)(20,27)(25,29)(28,33)(34,35,38,41)(36,39,44,42)(37,40,45,47)(43,46,49,48);(14,15,17,16)(18,20)(19,24)(21,26)(22,28)(23,27)(25,31)(29,32)(30,33)(34,35)(36,39)(37,40)(38,41)(42,44)(43,46)(45,47)(48,49);(18,21,23,19)(20,26,27,24)(22,29,30,25)(28,32,33,31)(34,36)(35,39)(37,43)(38,44)(40,46)(41,42)(45,49)(47,48);(14,16,17,15)(18,22)(19,25)(20,28)(21,29)(23,30)(24,31)(26,32)(27,33)(34,37,38,45)(35,40,41,47)(36,43,44,49)(39,46,42,48)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27514);