Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C27×C13 · Schur multiplier (H2) = C221 |
| direct product | C25×D4×C13 |
| unambiguous semidirect product | C4⋊(C26×C13) |
| unambiguous semidirect product | C22⋊(C26×C13) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C26×C13 | C22 |
| commutator, Frattini, cosocle | C2 | C27×C13 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C26×C13 ◁ G | |
111198 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 7 generators on 27 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27);(3,4);(5,6);(7,8);(9,10);(11,12,13,14);(12,14)2080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56083);