Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13×C16 · Schur multiplier (H2) = C22 |
| direct product | C13×#13640 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C13×C16 | C23 |
| commutator | C22 | C22×C13×C16 |
| Frattini, cosocle | C2×C16 | C23×C13 |
| socle | C22×C13 | C22×C16 |
| prime radical | C23×C13 | C2×C16 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C13×C16 ◁ G | |
194 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)(22,23,24,29,25,30,32,41,26,31,33,42,35,43,44,51,27,28,34,38,36,39,45,48,37,40,46,49,47,50,52,53);(15,18)(19,21);(14,16,17,20)(15,19,18,21)(23,28)(29,38)(30,39)(31,40)(41,48)(42,49)(43,50)(51,53)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6628);