Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C5 · Schur multiplier (H2) = C210 |
| direct product | C23×C5×C22⋊D5 |
| Fitting | C25×C52 ⋊ C2 |
| Sylow | C52 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24×C5 | C2×D5 |
| commutator, cosocle | C2×C5 | C25×C5 |
| Frattini | C2 | C24×C5×D5 |
| Fitting | C25×C52 | C2 |
| socle | C24×C52 | C22 |
| hypercenter | C25×C5 | D5 |
| hypocenter | C5 | C23×C5×D4 |
| LCS | G ▷ C2×C5 ▷ C5 | |
| UCS | C1 ◁ C24×C5 ◁ C25×C5 | |
3472 conjugacy classes of subgroups; only the 1086 normal subgroups are shown.
This group has 3472 conjugacy classes of subgroups — too many to draw. Only its 1086 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
520 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#87886 |
| maximal normal subgroup of | C23×#87886 |
| maximal quotient of | C5×#10619178 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10226);