Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C22×C13×#508 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | D8 |
| commutator, Frattini, cosocle | C8 | C25×C13 |
| socle | C23×C13 | C2×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
2118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2)(37,38,39,40,41,42,43,44,45,46,47,48,49);(3,4);(5,6)(7,16)(8,13)(9,21)(10,25)(11,15)(12,18)(14,23)(17,32)(19,33)(20,31)(22,27)(24,35)(26,30)(28,36)(29,34);(5,7)(6,12)(8,17)(9,22)(10,26)(11,19)(13,27)(14,30)(15,29)(16,21)(18,23)(20,34)(24,36)(25,28)(31,32)(33,35);(5,8,11,10)(6,13,15,25)(7,17,19,26)(9,20,24,23)(12,27,29,28)(14,21,31,35)(16,32,33,30)(18,22,34,36)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55616);