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) = C22×C4 |
| direct product | C13×#12839 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #427 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1808 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C13×M16 ◁ C2×C13×#131 ◁ G | |
362 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)(16,26)(17,32,34,22)(18,36)(19,39)(20,24)(21,29)(23,27)(25,37)(28,53,55,46)(30,59)(31,48)(33,63,65,66)(35,44,64,62)(38,67)(40,54,60,76)(41,58)(42,69)(43,51,61,73)(45,52)(47,50)(49,57)(56,71,75,74)(68,77,70,72);(14,16,27,50,19,30,38,58,20,31,52,69,37,57,18,29)(15,21,36,49,25,42,45,48,24,41,67,59,39,47,23,26)(17,28,51,72,35,56,65,76,34,55,73,77,64,75,33,54)(22,40,66,71,44,68,61,53,32,60,63,74,62,70,43,46);(14,17)(15,22)(16,28)(18,33)(19,35)(20,34)(21,40)(23,43)(24,32)(25,44)(26,46)(27,51)(29,54)(30,56)(31,55)(36,66)(37,64)(38,65)(39,62)(41,60)(42,68)(45,61)(47,70)(48,53)(49,71)(50,72)(52,73)(57,75)(58,76)(59,74)(63,67)(69,77)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5827);