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×#33572 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C13 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G | |
1108 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)(16,27)(17,25)(18,24)(19,34)(20,36)(21,26)(22,28)(23,32)(29,37)(30,44)(31,42)(33,41)(35,40)(38,43)(39,45);(14,16)(15,22)(17,28)(18,30)(19,35)(20,29)(21,31)(23,37)(24,39)(25,42)(26,40)(27,34)(32,45)(33,43)(36,38)(41,44);(14,17,21,19)(15,23,26,41)(16,28,31,35)(18,32,20,33)(22,37,40,44)(24,34,36,25)(27,38,42,39)(29,43,30,45);(14,18,21,20)(15,24,26,36)(16,29,31,30)(17,32,19,33)(22,38,40,39)(23,34,41,25)(27,37,42,44)(28,43,35,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26560);