Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×#6090 |
| derived, Sylow | C13 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D13 |
| commutator, hypocenter | C13 | C23×C16 |
| Frattini | C8 | C23×D13 |
| Fitting | C23×C8×C13 | C2 |
| socle, prime radical | C24×C13 | C8 |
| cosocle | C8×C13 | C24 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C23×C8 | |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
512 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13112913, C2×#13112914, #15777762, … |
| maximal normal subgroup of | C2×#13112913, C2×#13112914, #15777762, … |
| maximal quotient of | C22×C4×#6090, C22×C22⋊#6090, C22×C4⋊#6090, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17603);