Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | Q8×C4⋊#261 |
| Fitting | C4×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ Q8×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#261 |
| commutator, socle | C22×C13 | C23×C4 |
| Fitting | C4×Q8×C13 | C4 |
| prime radical, cosocle | C22×D13 | C24 |
| hypercenter | C4×Q8 | #261 |
| hypocenter | C13 | Q8×C4⋊C4 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
568 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 228 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | #16782593, #16782597, #16782601, … |
| maximal normal subgroup of | #16782593, #16782597, #16782601, … |
| maximal quotient of | C4⋊C4×C4⋊#261, Q8×(C2×#261)⋊C4, #16791651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21024);