Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#62171 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#529 ◁ G | |
1708 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21)(16,22,23,19)(17,25,26,20)(24,27,29,28)(30,31,34,38)(32,39,41,44)(33,37,35,42)(36,43,45,40);(14,16)(15,19)(17,24)(18,23)(20,27)(21,22)(25,28)(26,29)(30,31)(32,36)(33,42)(34,38)(35,37)(39,40)(41,45)(43,44);(30,32)(31,36)(33,40)(34,41)(35,43)(37,44)(38,45)(39,42);(16,23)(19,22)(24,29)(27,28)(30,33,34,35)(31,37,38,42)(32,40,41,43)(36,44,45,39);(14,17,18,26)(15,20,21,25)(16,24,23,29)(19,27,22,28)(31,38)(36,45)(37,42)(39,44)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55159);