Finite Group DatabasebetaFinite Group Databasebeta| order | 1208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D151 |
| Fitting | C22×C151 ⋊ C2 |
| Sylow | C151 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D151 |
| commutator, socle, cosocle | C2×C151 | C22 |
| Fitting | C22×C151 | C2 |
| hypercenter | C22 | D151 |
| hypocenter | C151 | D4 |
| LCS | G ▷ C2×C151 ▷ C151 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 155 |
| transitive degree | μt(G) = 604 |
Polycyclic presentation:
2^3,151|b^a=bc,d^b=d^150305 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D151, C2×C22⋊D151, #14559003, … |
| maximal normal subgroup of | D4×D151, C2×C22⋊D151, #14559003, … |
| maximal quotient of | (C2×D151)⋊C4, C22⋊Dic151, Dic151⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1208, 9);