Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2981 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D13 |
| commutator, socle | C22×C13 | C23×C4 |
| Fitting, prime radical | C13×#532 | C2 |
| cosocle | C2×C4×C13 | C24 |
| hypercenter | #532 | D13 |
| hypocenter | C13 | #2981 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
402 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,b^a=be,d^a=de,h^a=h^12,c^b=ceg,d^b=dg,d^c=dg212 conjugacy classes — view the full character table.
| maximal subgroup of | #15759504, #15759508, #15759518, … |
| maximal normal subgroup of | #15759504, #15759508, #15759518, … |
| maximal quotient of | #15861638, #15861672, #15861927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13586);