Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13101 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1898 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| prime radical | C2×C13×2−1+4 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×2−1+4 ◁ G | |
630 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)(14,15,20,26,21,27,19,25)(16,28,33,58,34,59,32,57)(17,35,38,23,39,51,37,52)(18,40,29,55,43,24,44,46)(22,45,48,41,49,67,54,31)(30,61,64,56,65,76,63,73)(36,70,60,50,42,69,71,53)(47,66,74,77,75,62,68,72);(14,16,29,45)(15,22,46,58)(17,30,60,72)(18,41,20,32)(19,33,43,31)(21,34,44,67)(23,47,69,61)(24,28,26,48)(25,54,40,59)(27,49,55,57)(35,68,53,56)(36,66,38,63)(37,64,42,62)(39,65,71,77)(50,73,51,74)(52,75,70,76);(14,17,21,39)(15,23,27,52)(16,30,34,65)(18,42,43,36)(19,38,20,37)(22,47,49,75)(24,53,40,50)(25,51,26,35)(28,56,59,73)(29,60,44,71)(31,66,41,62)(32,64,33,63)(45,72,67,77)(46,69,55,70)(48,68,54,74)(57,76,58,61)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6089);