Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3290 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C2×C13×#3293 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
2598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47);(3,4,10,15)(5,16,19,21)(6,18,11,25)(7,12,24,30)(8,14,9,13)(17,32,34,28)(20,33,27,22)(23,31,26,29);(3,5,10,19)(4,11,15,6)(7,22,24,33)(8,25,9,18)(12,28,30,32)(13,21,14,16)(17,26,34,23)(20,29,27,31);(3,6,10,11)(4,5,15,19)(7,20,24,27)(8,21,9,16)(12,17,30,34)(13,18,14,25)(22,31,33,29)(23,32,26,28);(3,7)(4,12)(5,17)(6,20)(8,26)(9,23)(10,24)(11,27)(13,31)(14,29)(15,30)(16,32)(18,33)(19,34)(21,28)(22,25)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54092);