Finite Group DatabasebetaFinite Group Databasebeta| order | 32192 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×D503 |
| Fitting | H(5,𝔽2)×C503 ⋊ C2 |
| Sylow | C503 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D503 |
| commutator, socle, cosocle | C2×C503 | C25 |
| Fitting | H(5,𝔽2)×C503 | C2 |
| hypercenter | H(5,𝔽2) | D503 |
| hypocenter | C503 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C503 ▷ C503 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
898 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4024 |
4301 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32192, 1378);