Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33557 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33560 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C13 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G | |
1132 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)(16,24)(17,21)(18,22)(19,23)(20,26)(25,38)(27,39)(28,42)(29,35)(30,36)(31,37)(32,40)(33,41)(34,43)(44,45);(14,16,19,27)(15,20,23,33)(17,28,29,25)(18,26,31,41)(21,34,35,32)(22,24,37,39)(30,43,44,40)(36,42,45,38);(17,29)(18,31)(21,35)(25,28)(26,41)(32,34)(36,45)(38,42);(14,17,19,29)(15,21,23,35)(16,25,27,28)(18,30,31,44)(20,32,33,34)(22,36,37,45)(24,38,39,42)(26,40,41,43)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26548);