Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C29 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | #1181 |
| commutator, hypocenter | C29 | C64 |
| Fitting | C16×C29 | C4 |
| socle, prime radical | C2×C29 | C32 |
| cosocle | #11745142 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C16 | |
14 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1856 |
Polycyclic presentation:
2^6,29|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^12,g^b=g^28176 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#14272002, D29⋊C64, #16834661, … |
| maximal normal subgroup of | C2×#14272002, D29⋊C64, #16834661, … |
| maximal quotient of | #16834307, C2×#14272002 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1388);