Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12925 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19)(20,31)(21,35)(22,29)(23,28)(24,30)(25,32)(26,33)(27,38)(34,46)(36,47)(37,41)(39,45)(40,44)(42,49)(43,48);(14,16,17,15)(18,20)(19,25)(21,36)(22,33)(23,40)(24,34)(26,41)(27,44)(28,42)(29,47)(30,43)(31,35)(32,38)(37,48)(39,49)(45,46);(18,20)(19,26)(21,32)(22,40)(23,33)(24,34)(25,41)(27,43)(28,46)(29,31)(30,44)(35,47)(36,38)(37,49)(39,48)(42,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5913);