Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23892 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23892 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26)(17,32)(18,36)(19,24)(20,25)(21,29)(22,34)(23,33)(27,43)(28,38)(30,40)(31,39)(35,42)(37,44)(41,45);(14,16)(15,21)(17,28)(18,30)(19,29)(20,31)(22,41)(23,38)(24,39)(25,40)(26,36)(27,33)(32,37)(34,44)(35,45)(42,43);(14,17)(15,22)(16,27)(18,33)(19,34)(20,35)(21,37)(23,25)(24,42)(26,38)(28,29)(30,45)(31,44)(32,36)(39,41)(40,43);(14,17)(15,23)(16,28)(18,34)(19,33)(20,35)(21,38)(22,25)(24,42)(26,37)(27,29)(30,44)(31,45)(32,36)(39,43)(40,41)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16880);