Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#95 ⋊ C4 |
| Sylow | C13 ⋊ #1442 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#261 |
| commutator, socle | C23×C13 | C22×C4 |
| Fitting | C13×#95 | C4 |
| prime radical, cosocle | C23×D13 | C23 |
| hypercenter | #95 | #261 |
| hypocenter | C13 | #1442 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #95 | |
520 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=e,c^2=d,b^a=bd,c^a=ce,h^a=h^8,c^b=cf,h^g=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16782560, #16782562, #16782563, … |
| maximal normal subgroup of | #16782560, #16782562, #16782563, … |
| maximal quotient of | #16778228, #16778230, #16786400, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19696);