Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7453 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#7454 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1365 |
| commutator | C2×C16 | C2×C4×C13 |
| Frattini, cosocle | C4×C16 | C22×C13 |
| prime radical | C22×C13 | #361 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C4×C8×C13 ◁ C4×C13×C16 ◁ G | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 2 generators on 77 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,25,43,27,38,24,19,46,44,56,49,55,41,75,22,28,39,60,20,47,40,57,21,26,45,59,37,62,17,36)(16,29,31,51,70,54,69,63,32,58,71,23,48,50,30,52,35,66,73,61,33,74,68,64,34,65,72,53,67,77,42,76);(14,16)(15,23,28,53)(17,31)(18,42)(19,34)(20,48)(21,32)(22,35)(24,54,57,74)(25,58,60,65)(26,61,46,51)(27,63,47,64)(29,59,66,56)(30,39)(33,49)(36,50,75,77)(37,70)(38,72)(40,71)(41,73)(43,67)(44,68)(45,69)(52,55,76,62)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 442);