Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#33793 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3169 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
538 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
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)(16,22)(17,20)(18,21)(19,24)(23,28)(25,27)(26,29)(30,31)(32,40)(33,38)(34,37)(35,36)(39,43)(41,44)(42,45);(14,16,18,24)(15,19,21,22)(17,25,26,23)(20,28,29,27)(30,32,33,35)(31,36,38,40)(34,41,42,43)(37,39,45,44);(14,17,18,26)(15,20,21,29)(16,23,24,25)(19,27,22,28)(31,37)(32,35)(34,43)(36,44)(38,45)(39,40)(41,42);(15,21)(19,22)(20,29)(27,28)(31,38)(36,40)(37,45)(39,44)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26781);