Finite Group DatabasebetaFinite Group Databasebeta| order | 1544 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊D193 |
| Fitting | C22×C193 ⋊ C2 |
| Sylow | C193 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D193 |
| commutator, socle, cosocle | C2×C193 | C22 |
| Fitting | C22×C193 | C2 |
| hypercenter | C22 | D193 |
| hypocenter | C193 | D4 |
| LCS | G ▷ C2×C193 ▷ C193 | |
| UCS | C1 ◁ C2 ◁ C22 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 197 |
| transitive degree | μt(G) = 772 |
Polycyclic presentation:
2^3,193|b^a=bc,d^b=d^192389 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D193, C2×C22⋊D193, #15690554, … |
| maximal normal subgroup of | D4×D193, C2×C22⋊D193, #15690554, … |
| maximal quotient of | #15690532, C22⋊Dic193, #15690534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1544, 9);