Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C2×C13×#3287 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C4×D4×C13 ◁ G | |
2910 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4)(5,6)(8,13)(9,11)(10,17)(14,18)(15,19)(21,22);(7,8,12,15)(9,13,11,19)(10,18,17,21)(14,20,22,16);(4,6)(7,9,12,11)(8,13,15,19)(10,16,17,20)(14,21,22,18);(7,10,12,17)(8,14,15,22)(9,16,11,20)(13,21,19,18)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54035);