Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×#1057 |
| derived, Sylow | C13 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #261 |
| commutator, hypocenter | C13 | C24×C8 |
| Frattini | C2 | C24×#261 |
| Fitting, socle, prime radical | C25×C13 | C4 |
| cosocle | Dic13 | C25 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C25 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | #16785258, C22×#11718290, C2×#13130502, … |
| maximal normal subgroup of | #16785258, C22×#11718290, C2×#13130502, … |
| maximal quotient of | C23×C4×#1057, C23×C22⋊#1057, C23×C4⋊#1057, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21493);