Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×#6092 |
| derived, Sylow | C13 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #261 |
| commutator, hypocenter | C13 | C23×C16 |
| Frattini | C4 | C23×#261 |
| Fitting | C23×C4×C13 | C4 |
| socle, prime radical | C24×C13 | C8 |
| cosocle | #1055 | C24 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C23×C4 | |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129874, C2×#13129875, #16789048, … |
| maximal normal subgroup of | C2×#13129874, C2×#13129875, #16789048, … |
| maximal quotient of | C22×C4×#6092, C22×C22⋊#6092, C22×C4⋊#6092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21469);