Finite Group DatabasebetaFinite Group Databasebeta| order | 1856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C42×C29 ⋊ C4 |
| Sylow | C29 ⋊ #382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#1181 |
| commutator, socle | C22×C29 | C22×C4 |
| Fitting | C42×C29 | C4 |
| prime radical, cosocle | C22×D29 | C23 |
| hypercenter | C42 | #1181 |
| hypocenter | C29 | #382 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C42 | |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^6,29|a^2=f,b^2=e,c^2=d,b^a=bd,c^a=ce,g^a=g^12,g^f=g^28140 conjugacy classes — view the full character table.
| maximal subgroup of | #16834346, #16834347, #16834369, … |
| maximal normal subgroup of | #16834346, #16834347, #16834369, … |
| maximal quotient of | #16834668, #16834670, #16834678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1856, 1493);