Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33571 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C13 |
| prime radical | C13×#3018 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G | |
1084 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26)(17,23)(18,32)(19,22)(20,25)(21,28)(24,35)(27,38)(29,42)(30,41)(31,39)(33,40)(34,43)(36,45)(37,44);(14,16,20,30)(15,21,25,38)(17,28,18,27)(19,34,35,29)(22,36,24,37)(23,41,32,26)(31,44,33,45)(39,43,40,42);(15,22)(19,35)(21,36)(23,39)(24,25)(26,42)(29,34)(31,33)(32,40)(37,38)(41,43)(44,45);(14,17,20,18)(15,23,25,32)(16,27,30,28)(19,31,35,33)(21,26,38,41)(22,39,24,40)(29,44,34,45)(36,42,37,43)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26559);