Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#12613 |
| subgroup | G/H | |
|---|---|---|
| center | C13×C16 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | C8×C22⋊C4 |
| prime radical | C2×C13×#41 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C13×C16 ◁ C22×C13×C16 ◁ G | |
410 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,23,19,25,34,45,20,24,35,44,36,46,58,67)(16,26,29,48,30,49,54,70,28,21,37,39,53,40,60,63)(17,22,31,41,32,43,55,65,33,42,56,64,57,66,73,76)(27,47,51,68,52,69,72,77,50,38,59,61,71,62,74,75);(14,16)(15,21,24,26)(17,27)(18,29)(19,30)(20,28)(22,38,42,47)(23,39,44,48)(25,40,46,49)(31,51)(32,52)(33,50)(34,54)(35,37)(36,53)(41,61,64,68)(43,62,66,69)(45,63,67,70)(55,72)(56,59)(57,71)(58,60)(65,75,76,77)(73,74);(14,17,18,31,19,32,34,55,20,33,35,56,36,57,58,73)(15,22,23,41,25,43,45,65,24,42,44,64,46,66,67,76)(16,27,29,51,30,52,54,72,28,50,37,59,53,71,60,74)(21,38,39,61,40,62,63,75,26,47,48,68,49,69,70,77)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5601);