Finite Group DatabasebetaFinite Group Databasebeta| order | 848 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D53⋊C8 |
| derived, Sylow | C53 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #6157 |
| commutator, hypocenter | C53 | C2×C8 |
| Frattini | C2 | C2×#6157 |
| Fitting | C4×C53 | C4 |
| socle | C2×C53 | C2×C4 |
| prime radical | C2×D53 | C4 |
| cosocle | Dic53 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
Polycyclic presentation:
2^4,53|a^2=c,b^2=d,c^2=d,e^a=e^30,e^c=e^5268 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#6157, #13133271, #13133279, … |
| maximal normal subgroup of | C8×#6157, #13133271, #13133279, … |
| maximal quotient of | C4×#88324, #13133274, #13133284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 28);