Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C5 |
| direct product | C23×C22⋊(C5⋊D5) |
| Fitting | C25×C52 ⋊ C2 |
| Sylow | C52 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×C5⋊D5 |
| commutator, cosocle | C2×C52 | C25 |
| Frattini | C2 | C24×C5⋊D5 |
| Fitting | C25×C52 | C2 |
| socle | C24×C52 | C22 |
| hypercenter | C25 | C5⋊D5 |
| hypocenter | C52 | C23×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C24 ◁ C25 | |
5448 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×D4×C5⋊D5, #72221188 |
| maximal normal subgroup of | C23×D4×C5⋊D5, #72221188 |
| maximal quotient of | #72221198, #72221199, #72221201 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10246);