Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10238 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10249 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C22×D4×C13 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
536 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
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)(16,20)(17,19)(18,22)(21,25)(23,28)(24,29)(26,27)(30,31,35,39)(32,40,42,45)(33,38,34,37)(36,43,44,41);(15,19)(17,25)(20,28)(21,22)(23,26)(27,29)(30,32)(31,36)(33,43)(34,41)(35,42)(37,45)(38,40)(39,44);(14,16,18,24)(15,20,22,29)(17,26,25,23)(19,27,21,28)(31,37)(33,34)(36,40)(38,39)(41,43)(44,45)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3237);