Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#17352 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C22 | C23×C8×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C22×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C4×Q8×C13 ◁ G | |
1162 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,18,17,19,20,21)(22,23)(24,32,35,28)(25,29)(26,30)(27,31)(33,46,49,40)(34,47,51,41)(36,42)(37,43)(38,44)(39,45)(48,53,50,52);(22,24)(23,28)(25,33)(26,34)(27,35)(29,40)(30,41)(31,32)(36,48)(37,49)(38,50)(39,51)(42,52)(43,46)(44,53)(45,47);(22,25,27,37)(23,29,31,43)(24,33,35,49)(26,38,39,36)(28,40,32,46)(30,44,45,42)(34,50,51,48)(41,53,47,52);(22,26,27,39)(23,30,31,45)(24,34,35,51)(25,36,37,38)(28,41,32,47)(29,42,43,44)(33,48,49,50)(40,52,46,53)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10340);