Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#11719282 |
| Fitting | C2×C4×Q8×C13 ⋊ C2 |
| Sylow | C13 ⋊ C2×#550 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D13 |
| commutator, cosocle | C22×C13 | C25 |
| Frattini | C22 | C24×D13 |
| Fitting | C2×C4×Q8×C13 | C2 |
| socle | C23×C13 | C24 |
| hypercenter | C2×C4×Q8 | D13 |
| hypocenter | C13 | C2×#550 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
1736 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 581 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15754625, #15754628, #15754631, … |
| maximal normal subgroup of | #15754625, #15754628, #15754631, … |
| maximal quotient of | C2×#13117674, C2×Q8×C4⋊Dic13, C2×#13117783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17991);