Finite Group DatabasebetaFinite Group Databasebeta| order | 848 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D53 |
| unambiguous semidirect product | C53⋊C24 |
| unambiguous semidirect product | (C2×C53)⋊C23 |
| Fitting, socle | C23×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D53 |
| commutator, cosocle, hypocenter | C53 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C53 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D53, C2×#11719921, #13133185, … |
| maximal normal subgroup of | C22⋊C4×D53, C2×#11719921, #13133185, … |
| maximal quotient of | C22×C4×D53, C23×Dic53, C2×D4×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(848, 50);