Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C13×C4⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ #2522 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D13 |
| commutator, socle, cosocle | C23×C13 | C24 |
| Fitting | C4×C13×C4⋊C4 | C2 |
| prime radical | C23×D13 | C23 |
| hypercenter | C4×C4⋊C4 | D13 |
| hypocenter | C13 | #2522 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C4×C4⋊C4 | |
428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=eg,b^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^12278 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2522, C2×#13119548, #16032190, … |
| maximal normal subgroup of | D13×#2522, C2×#13119548, #16032190, … |
| maximal quotient of | #15785013, #15785365, #15786217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 9222);