Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×#496 ⋊ C2 |
| Sylow | C13 ⋊ #1656 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #88191 |
| commutator, cosocle | C42×C13 | C23 |
| Frattini | C42 | C22×D13 |
| Fitting | C13×#496 | C2 |
| socle | C22×C13 | #120 |
| hypercenter | #496 | D13 |
| hypocenter | C13 | #1656 |
| LCS | G ▷ C42×C13 ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #496 | |
230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=f,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,d^b=df,e^b=eg,d^c=dg,e^c=efg,h^c=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1656, C2×#13114127, #15844068, … |
| maximal normal subgroup of | D13×#1656, C2×#13114127, #15844068, … |
| maximal quotient of | #15751619, #15751620, #15751632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 3801);