Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12741 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#12743 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1786 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#576 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,25,20,24,19,36)(16,26,28,42,29,22,35,41)(17,30,32,43,34,37,33,23)(21,31,39,44,38,45,40,27);(14,16)(15,21)(17,31)(18,28)(19,35)(20,29)(22,37)(23,41)(24,38)(25,39)(26,30)(27,33)(32,44)(34,45)(36,40)(42,43);(14,16)(15,22)(17,27)(18,35)(19,28)(20,29)(21,37)(23,40)(24,26)(25,42)(30,38)(31,33)(32,45)(34,44)(36,41)(39,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5731);