Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C29 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#1181 |
| commutator, socle | C2×C29 | C22×C8 |
| Fitting | M16×C29 | C4 |
| prime radical | #90805 | C4 |
| cosocle | #6597 | C23 |
| hypercenter | M16 | #1181 |
| hypocenter | C29 | #504 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C4 ◁ M16 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=d,d^2=e,e^2=f,g^a=g^12,c^b=cf,g^b=g^28,g^d=g^28110 conjugacy classes — view the full character table.
| maximal subgroup of | #16835880, #16835881, #16835883, … |
| maximal normal subgroup of | #16835880, #16835881, #16835883, … |
| maximal quotient of | #16835702, #16835703, #16835723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1608);