Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #62636 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#62636 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C23×D8 |
| commutator, Frattini, cosocle | C8 | C25×C13 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C13×#41 ◁ C2×C13×#131 ◁ G | |
2078 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
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)(16,21)(17,20)(18,31)(19,22)(23,28)(24,29)(25,35)(26,32)(27,41)(30,33)(34,42)(36,40)(37,39)(38,43)(44,45);(15,20)(17,28)(18,29)(21,32)(22,33)(23,24)(26,40)(27,39)(30,42)(31,34)(35,43)(36,37)(38,45)(41,44);(14,16)(15,21)(17,26)(18,27)(19,25)(20,32)(22,35)(23,36)(24,37)(28,40)(29,39)(30,38)(31,41)(33,43)(34,44)(42,45);(16,25)(21,35)(26,38)(27,39)(32,43)(36,44)(37,41)(40,45);(15,22)(20,33)(21,35)(23,34)(24,31)(32,43)(36,44)(37,41)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55624);