Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C13×#127 ⋊ C2 |
| Sylow | C13 ⋊ #3508 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D13 |
| commutator, socle, cosocle | C22×C13 | C25 |
| Fitting | C2×C13×#127 | C2 |
| hypercenter | C2×#127 | D13 |
| hypocenter | C13 | #3508 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C2×#127 | |
1232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15754870, #15754874, #15755151, … |
| maximal normal subgroup of | #15754870, #15754874, #15755151, … |
| maximal quotient of | #16023063, #16023325, #16023368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18384);