Finite Group DatabasebetaFinite Group Databasebeta| order | 32272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D2017 |
| unambiguous semidirect product | C23⋊D2017 |
| Fitting | C23×C2017 ⋊ C2 |
| Sylow | C2017 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D2017 |
| commutator, cosocle | C2×C2017 | C23 |
| Frattini | C2 | C22×D2017 |
| Fitting | C23×C2017 | C2 |
| socle | C22×C2017 | C22 |
| hypercenter | C23 | D2017 |
| hypocenter | C2017 | C2×D4 |
| LCS | G ▷ C2×C2017 ▷ C2017 | |
| UCS | C1 ◁ C22 ◁ C23 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16136 |
8074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32272, 35);