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 | C4⋊C4×C29 | C4 |
| cosocle | C2×Dic29 | C23 |
| hypercenter | C4⋊C4 | #1181 |
| hypocenter | C29 | #446 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
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^b=g^28,g^c=g^12,g^e=g^2898 conjugacy classes — view the full character table.
| maximal subgroup of | D29⋊#446, C2×#14272215, #16836280, … |
| maximal normal subgroup of | D29⋊#446, C2×#14272215, #16836280, … |
| maximal quotient of | #16835287, #16835291, #16835292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1601);