Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C29 ⋊ #446 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#1181 |
| commutator, socle, prime radical | C22×C29 | C22×C4 |
| Fitting | C2×Q8×C29 | C4 |
| cosocle | C2×Dic29 | C23 |
| hypercenter | C2×Q8 | #1181 |
| hypocenter | C29 | #446 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=e,b^2=d,c^2=de,e^2=f,b^a=bd,c^a=cf,g^a=g^17,g^c=g^12,g^e=g^2898 conjugacy classes — view the full character table.
| maximal subgroup of | #16835097, #16835098, #16835105, … |
| maximal normal subgroup of | #16835097, #16835098, #16835105, … |
| maximal quotient of | #16835288, #16835292, #16835548, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1600);