Finite Group DatabasebetaFinite Group Databasebeta| order | 848 |
| isoclinism | isoclinic class of Dic106 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D53 |
| unambiguous semidirect product | C23⋊D53 |
| Fitting | C23×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D53 |
| commutator, cosocle | C2×C53 | C23 |
| Frattini | C2 | C22×D53 |
| Fitting | C23×C53 | C2 |
| socle | C22×C53 | C22 |
| hypercenter | C23 | D53 |
| hypocenter | C53 | C2×D4 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C23 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
218 conjugacy classes — view the full character table.
| maximal subgroup of | #13133131, #13133177, C4×C22⋊D53, … |
| maximal normal subgroup of | #13133131, #13133177, C4×C22⋊D53, … |
| maximal quotient of | C2×#11719921, C2×C22⋊Dic53, C2×#11719919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 44);