Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
No aliases for this group.
| Fitting | C13×#585 ⋊ C2 |
| Sylow | C13 ⋊ H(7,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×D13 |
| commutator, socle, cosocle | C2×C13 | C26 |
| Fitting | C13×#585 | C2 |
| hypercenter | #585 | D13 |
| hypocenter | C13 | H(7,𝔽2) |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ #585 | |
5992 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.
This group has 5992 conjugacy classes of subgroups — too many to draw. Only its 3201 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=bg,f^a=fg,e^b=eg,d^c=dg,h^e=h^12,h^f=h^12269 conjugacy classes — view the full character table.
| maximal subgroup of | #16011660, #16011662, #16011664, … |
| maximal normal subgroup of | #16011660, #16011662, #16011664, … |
| maximal quotient of | #16769535, #16769537, #16769544, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19321);