Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C29 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×#1181 |
| commutator, socle | C2×C29 | C2×C16 |
| Fitting | C16×C29 | C4 |
| prime radical | C2×D29 | C16 |
| cosocle | #90768 | C22 |
| hypercenter | C16 | #1181 |
| hypocenter | C29 | M64 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C8 ◁ C16 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 928 |
Polycyclic presentation:
2^6,29|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^12,g^b=g^28,g^c=g^28152 conjugacy classes — view the full character table.
| maximal subgroup of | #16834601, #16834602, #16834645, … |
| maximal normal subgroup of | #16834601, #16834602, #16834645, … |
| maximal quotient of | #16834600, #16834606, #16834650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1482);