Finite Group DatabasebetaFinite Group Databasebeta| order | 848 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#6157 |
| unambiguous semidirect product | (C2×#6157)⋊C2 |
| Fitting | C22×C53 ⋊ C4 |
| Sylow | C53 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#6157 |
| commutator, socle | C2×C53 | C2×C4 |
| Fitting | C22×C53 | C4 |
| prime radical | C22×D53 | C2 |
| cosocle | C2×D53 | C22 |
| hypercenter | C22 | #6157 |
| hypocenter | C53 | C22⋊C4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C22 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 212 |
Polycyclic presentation:
2^4,53|a^2=c,b^a=bd,e^a=e^30,e^c=e^5262 conjugacy classes — view the full character table.
| maximal subgroup of | #13133275, #13133276, C2×C22⋊#6157, … |
| maximal normal subgroup of | #13133275, #13133276, C2×C22⋊#6157, … |
| maximal quotient of | (C2×#6157)⋊C4, C22⋊#88324, #13133274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 34);