Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13539 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,20)(16,21,17,19)(22,23)(24,26)(25,27)(28,29)(30,31,33,35)(32,36,39,43)(34,37,41,42)(38,44,45,40);(14,16,18,17)(15,19,20,21)(22,24,25,28)(23,26,27,29)(30,32,33,39)(31,36,35,43)(34,38,41,45)(37,44,42,40);(14,17,18,16)(15,19,20,21)(23,27)(26,29)(31,35)(32,38)(34,42)(36,40)(37,41)(39,45)(43,44)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6527);