Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#11719416 |
| Fitting | C2×C13×#126 ⋊ C2 |
| Sylow | C13 ⋊ C2×#560 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D13 |
| commutator, cosocle | C22×C13 | C25 |
| Frattini | C22 | C24×D13 |
| Fitting | C2×C13×#126 | C2 |
| socle | C23×C13 | C24 |
| hypercenter | C2×#126 | D13 |
| hypocenter | C13 | C2×#560 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×#126 | |
1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
206 conjugacy classes — view the full character table.
| maximal subgroup of | #16025606, C4×#11719416, #16028723, … |
| maximal normal subgroup of | #16025606, C4×#11719416, #16028723, … |
| maximal quotient of | C2×#13117976, C2×#13117983, C2×#13117989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18628);