Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13×C16 · Schur multiplier (H2) = C25 |
| direct product | C13×#33974 |
| subgroup | G/H | |
|---|---|---|
| center | C13×C16 | C24 |
| commutator | C2 | C23×C13×C16 |
| Frattini, cosocle | C16 | C24×C13 |
| socle | C2×C13 | C23×C16 |
| prime radical | C2×C13×#41 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C13×C16 ◁ G | |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,23,18,24,30,43,19,25,31,44,33,45,52,65,20,22,32,40,34,41,53,62,35,42,54,63,55,64,70,75)(16,21,27,37,28,38,49,59,29,39,50,60,51,61,69,74,26,36,46,56,47,57,66,71,48,58,67,72,68,73,76,77);(14,16)(15,21)(17,27)(18,28)(19,29)(20,26)(22,36)(23,37)(24,38)(25,39)(30,49)(31,50)(32,46)(33,51)(34,47)(35,48)(40,56)(41,57)(42,58)(43,59)(44,60)(45,61)(52,69)(53,66)(54,67)(55,68)(62,71)(63,72)(64,73)(65,74)(70,76)(75,77);(16,26)(21,36)(27,46)(28,47)(29,48)(37,56)(38,57)(39,58)(49,66)(50,67)(51,68)(59,71)(60,72)(61,73)(69,76)(74,77);(15,22)(21,36)(23,40)(24,41)(25,42)(37,56)(38,57)(39,58)(43,62)(44,63)(45,64)(59,71)(60,72)(61,73)(65,75)(74,77)1768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26962);