Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33551 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33556 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C13 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G | |
1134 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)(17,22)(18,23)(19,24)(20,25)(21,28)(27,40)(29,41)(30,36)(31,45)(32,38)(33,39)(34,42)(35,44)(37,43);(14,16,20,29)(15,21,25,35)(17,27,18,31)(19,28,33,44)(22,34,23,37)(24,26,39,41)(30,42,32,43)(36,40,38,45);(14,17,20,18)(15,22,25,23)(16,27,29,31)(19,32,33,30)(21,34,35,37)(24,36,39,38)(26,40,41,45)(28,43,44,42);(14,18,20,17)(15,23,25,22)(16,27,29,31)(19,32,33,30)(21,34,35,37)(24,38,39,36)(26,40,41,45)(28,42,44,43)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26544);