Finite Group DatabasebetaFinite Group Databasebeta| order | 848 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D53 |
| Fitting | C8×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D53 |
| commutator, hypocenter | C53 | C2×C8 |
| Frattini | C4 | C2×D53 |
| Fitting | C8×C53 | C2 |
| socle | C2×C53 | C2×C4 |
| prime radical | C2×D53 | C4 |
| cosocle | C4×C53 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C16×D53, #13133156, C2×C8×D53, … |
| maximal normal subgroup of | C16×D53, #13133156, C2×C8×D53, … |
| maximal quotient of | C8×Dic53, #13133129, #13133146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 4);