Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D5×#4144 |
| Fitting | C2×C52×D4 ⋊ C22 |
| Sylow | C52 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D52 |
| commutator, socle, cosocle | C2×C52 | C25 |
| Fitting | C2×C52×D4 | C22 |
| hypercenter | C2×D4 | D52 |
| hypocenter | C52 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
1962 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
148 conjugacy classes — view the full character table.
| maximal subgroup of | D52×H(5,𝔽2) |
| maximal normal subgroup of | D52×H(5,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10172);