Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#7426 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1351 |
| commutator | C2×C22⋊C4 | C2×C4×C13 |
| Frattini, cosocle | #379 | C22×C13 |
| prime radical | C25×C13 | D4 |
| LCS | G ▷ C2×C22⋊C4 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C23×C13 ◁ C24×C13 ◁ C13×#379 ◁ G | |
332 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 208 |
A minimal faithful permutation representation — 2 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22)(17,25)(18,21)(19,23,28,26)(20,27)(24,29);(14,16)(15,19)(17,26,27,23)(18,24)(20,22,25,29)(21,28)325 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 414);