Finite Group DatabasebetaFinite Group Databasebeta| order | 808 |
| isoclinism | isoclinic class of D101 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D101 |
| unambiguous semidirect product | C101⋊C23 |
| unambiguous semidirect product | (C2×C101)⋊C22 |
| Fitting, socle | C22×C101 ⋊ C2 |
| derived, Sylow | C101 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D101 |
| commutator, cosocle, hypocenter | C101 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C22×C101 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C22 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 404 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #13108051, C2×C4×D101, D4×D101, … |
| maximal normal subgroup of | #13108051, C2×C4×D101, D4×D101, … |
| maximal quotient of | C2×C4×D101, C22×Dic101, D4×D101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(808, 13);