Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#2218 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
516 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,19)(17,18)(20,21)(22,23)(24,29)(25,35)(26,40)(27,42)(28,32)(30,39)(31,37)(33,47)(34,46)(36,49)(38,50)(41,53)(43,48)(44,51)(45,52);(15,18)(19,21)(22,24,28,27)(23,29,32,42)(25,36,38,33)(26,34,41,37)(30,44,45,43)(31,40,46,53)(35,49,50,47)(39,51,52,48);(22,25,37,51,27,36,41,52,28,38,34,48,24,33,26,39)(23,30,40,47,29,43,46,50,32,45,53,49,42,44,31,35);(14,16,17,20)(15,19,18,21)(25,38)(30,45)(33,36)(35,50)(39,52)(43,44)(47,49)(48,51)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26738);