Finite Group DatabasebetaFinite Group Databasebeta| order | 848 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D53 |
| commutator, cosocle | C4×C53 | C22 |
| Frattini | C4 | C2×D53 |
| Fitting | Q8×C53 | C2 |
| socle | C2×C53 | D4 |
| prime radical | D212 | C2 |
| hypercenter | Q8 | D53 |
| hypocenter | C53 | SD16 |
| LCS | G ▷ C4×C53 ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 424 |
Polycyclic presentation:
2^4,53|b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^52,c^b=cd137 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D53, C2×#11719924, #13133237, … |
| maximal normal subgroup of | SD16×D53, C2×#11719924, #13133237, … |
| maximal quotient of | #13133137, #13133141, #13133148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 17);