Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C13×H(5,𝔽2) ⋊ C2 |
| Sylow | C13 ⋊ #3496 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | C2×C13×H(5,𝔽2) | C2 |
| hypercenter | C2×H(5,𝔽2) | D13 |
| hypocenter | C13 | #3496 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
1660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|c^2=g,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^12248 conjugacy classes — view the full character table.
| maximal subgroup of | #15898111, #15898113, #15898129, … |
| maximal normal subgroup of | #15898111, #15898113, #15898129, … |
| maximal quotient of | #16023005, #16023265, #16023277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18269);