Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12753 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#12754 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1790 |
| commutator | C2×D4 | C22×C4×C13 |
| Frattini, cosocle | C22×D4 | C23×C13 |
| prime radical | C13×#3533 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C23×C13 ◁ C22×D4×C13 ◁ G | |
782 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
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)(16,24)(17,21)(18,30,31,22)(19,23)(20,26,33,42)(25,39)(27,38)(28,36,43,34)(29,35)(32,40,44,45)(37,41);(14,16)(15,20)(17,25)(18,26)(19,27)(21,32)(22,24)(23,33)(28,40)(29,41)(30,38)(31,42)(34,39)(35,44)(36,37)(43,45);(14,17,19,29)(15,21,23,35)(16,25,27,41)(18,28,31,43)(20,32,33,44)(22,36,30,34)(24,37,38,39)(26,40,42,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5742);