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×#33561 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C13 |
| prime radical | C13×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#41 ◁ G | |
1096 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)(17,22)(18,23)(19,24)(20,25)(21,28)(27,38)(29,36)(30,35)(31,39)(32,40)(33,41)(34,42)(37,43)(44,45);(14,16,20,17)(15,21,25,35)(18,29,32,27)(19,28,33,30)(22,24,26,41)(23,37,40,34)(31,43,44,42)(36,45,38,39);(14,17,20,16)(15,22,25,26)(18,27,32,29)(19,28,33,30)(21,24,35,41)(23,38,40,36)(31,43,44,42)(34,45,37,39);(14,18,20,32)(15,23,25,40)(16,27,17,29)(19,31,33,44)(21,34,35,37)(22,36,26,38)(24,39,41,45)(28,42,30,43)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26549);