Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12026 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#12911 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #427 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1846 |
| prime radical | C23×C13 | #135 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
266 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)(16,27,31,51)(17,33,36,63)(18,38)(19,25)(20,42)(21,26)(22,29,45,58)(23,35,47,37)(24,40)(28,52)(30,50,32,60)(34,64,66,46)(39,48)(41,68)(43,70)(44,57,69,59)(49,55)(53,74)(54,72)(56,73)(61,76)(62,65,77,67)(71,75);(14,16,18,29,20,32,40,59,21,31,41,58,19,30,39,57)(15,22,24,27,25,44,38,50,26,45,48,51,42,69,68,60)(17,28,34,53,37,55,67,75,36,56,66,76,35,54,65,70)(23,43,46,49,33,61,62,52,47,71,64,72,63,74,77,73);(14,17)(15,23,26,47)(16,28)(18,34)(19,35)(20,37)(21,36)(22,43,45,71)(24,46,48,64)(25,33,42,63)(27,49,51,72)(29,53)(30,54)(31,56)(32,55)(38,62,68,77)(39,65)(40,67)(41,66)(44,61,69,74)(50,52,60,73)(57,70)(58,76)(59,75)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5899);