Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2581 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, prime radical, cosocle | C23×C13 | C24 |
| Fitting | C2×C4×Q8×C13 | C2 |
| hypercenter | C2×C4×Q8 | D13 |
| hypocenter | C13 | #2581 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
468 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 169 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=e,b^2=g,c^2=g,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^12278 conjugacy classes — view the full character table.
| maximal subgroup of | #15760761, #15760763, #15760781, … |
| maximal normal subgroup of | #15760761, #15760763, #15760781, … |
| maximal quotient of | #15785323, #15785478, #15786299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 9872);