Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C214 |
| direct product | C13×#63090 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C23×D4 |
| commutator, Frattini, cosocle | C4 | C26×C13 |
| socle | C2×C13 | C24×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C13×#41 ◁ G | |
10836 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,25)(17,22)(18,24)(19,32)(20,23)(21,27)(26,39)(28,36)(29,37)(30,38)(31,42)(33,35)(34,41)(40,45)(43,44);(14,16)(15,21)(17,26)(18,27)(19,33)(20,28)(22,34)(23,35)(24,36)(25,32)(29,40)(30,41)(31,43)(37,44)(38,45)(39,42);(14,17)(15,22)(16,26)(18,30)(19,31)(20,29)(21,34)(23,37)(24,38)(25,39)(27,41)(28,40)(32,42)(33,43)(35,44)(36,45);(17,29)(22,37)(26,40)(30,31)(34,44)(38,42)(39,45)(41,43);(15,23)(21,35)(22,37)(24,32)(25,36)(34,44)(38,42)(39,45);(14,18,20,19)(15,24,23,32)(16,27,28,33)(17,30,29,31)(21,36,35,25)(22,38,37,42)(26,41,40,43)(34,45,44,39)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56078);