Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61109 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61109 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
2626 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)(16,27)(17,23)(18,26)(19,25)(20,24)(21,31)(22,32)(28,36)(29,43)(30,42)(33,41)(34,38)(35,39)(37,44)(40,45);(14,16)(15,21)(17,28)(18,34)(19,31)(20,30)(22,36)(23,40)(24,38)(25,42)(26,27)(29,32)(33,44)(35,45)(37,39)(41,43);(14,17)(15,22)(16,28)(18,32)(19,35)(20,33)(21,36)(23,25)(24,39)(26,41)(27,43)(29,34)(30,44)(31,45)(37,38)(40,42);(14,17)(15,23)(16,29)(18,35)(19,32)(20,33)(21,37)(22,25)(24,41)(26,39)(27,43)(28,34)(30,45)(31,44)(36,38)(40,42);(15,24)(16,30)(22,39)(23,41)(25,26)(28,44)(29,45)(31,34)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54097);