Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #2809 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, prime radical, cosocle | C23×C13 | C24 |
| Fitting | C13×#391 | C2 |
| hypercenter | #391 | D13 |
| hypocenter | C13 | #2809 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #391 | |
368 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=eg,b^2=ef,c^2=fg,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^12,h^d=h^12200 conjugacy classes — view the full character table.
| maximal subgroup of | #15782067, #15782068, #15782607, … |
| maximal normal subgroup of | #15782067, #15782068, #15782607, … |
| maximal quotient of | #15791389, #15791610, #15791612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 12496);