Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13×C32 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#13639 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13×C16 | C22 |
| commutator | C2 | C22×C13×C32 |
| Frattini, cosocle | C2×C16 | C23×C13 |
| socle | C22×C13 | C22×C16 |
| prime radical | C23×C13 | C2×C16 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13×C16 ◁ G | |
202 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23,24,28,25,29,32,38,26,30,33,39,35,41,44,48,27,31,34,40,36,42,45,49,37,43,46,50,47,51,52,53);(15,18)(19,21);(14,16,17,20)(15,19,18,21)2080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6627);