Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#534 ⋊ C2 |
| Sylow | C13 ⋊ #2021 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #88207 |
| commutator, cosocle | C24×C13 | C23 |
| Frattini | C24 | C22×D13 |
| Fitting | C13×#534 | C2 |
| socle | C22×C13 | #120 |
| hypercenter | #534 | D13 |
| hypocenter | C13 | #2021 |
| LCS | G ▷ C24×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #534 | |
638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|b^a=bd,c^a=ce,f^a=fg,c^b=cf,h^b=h^12,d^c=dg158 conjugacy classes — view the full character table.
| maximal subgroup of | #15774946, #15774951, #15774963, … |
| maximal normal subgroup of | #15774946, #15774951, #15774963, … |
| maximal quotient of | #15763113, #15763120, #15763127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5634);