Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62781 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| socle | C22×C13 | C26 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ G | |
7230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23)(24,27)(25,32)(26,29)(28,33)(30,36)(31,35)(34,37);(15,18)(19,21)(22,24,26,31)(23,27,29,35)(25,30,33,37)(28,34,32,36);(22,25)(23,28)(24,30)(26,33)(27,34)(29,32)(31,37)(35,36);(25,33)(28,32)(30,37)(34,36);(23,29)(27,35)(28,32)(34,36);(14,16,17,20)(15,19,18,21)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55769);