Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C2×C13×#2262 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | D16 |
| commutator, Frattini, cosocle | C16 | C24×C13 |
| socle | C22×C13 | C2×D16 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C4×C13 ◁ C22×C8×C13 ◁ C22×C13×C16 ◁ G | |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 79 points:
(1,2)(67,68,69,70,71,72,73,74,75,76,77,78,79);(3,4)(5,16)(6,11)(7,25)(8,29)(9,15)(10,18)(12,27)(13,23)(14,24)(17,43)(19,49)(20,51)(21,44)(22,52)(26,40)(28,58)(30,37)(31,36)(32,45)(33,59)(34,48)(35,54)(38,64)(39,61)(41,56)(42,47)(46,63)(50,65)(53,62)(55,57)(60,66);(3,5)(4,10)(6,17)(7,26)(8,30)(9,21)(11,32)(12,37)(13,40)(14,42)(15,34)(16,25)(18,27)(19,23)(20,24)(22,53)(28,60)(29,33)(31,46)(35,49)(36,62)(38,65)(39,63)(41,66)(43,52)(44,58)(45,54)(47,64)(48,61)(50,56)(51,57)(55,59);(3,6,9,24)(4,11,15,14)(5,17,21,20)(7,22,28,55)(8,23,31,56)(10,32,34,42)(12,35,39,38)(13,36,41,29)(16,43,44,51)(18,45,48,47)(19,46,50,30)(25,52,58,57)(26,53,60,59)(27,54,61,64)(33,40,62,66)(37,49,63,65)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26966);