Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C27 |
| direct product | C2×C5×#4099 |
| Fitting | C25×C52 ⋊ C2 |
| Sylow | C52 ⋊ C2×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C5 | C22×D5 |
| commutator, cosocle | C22×C5 | C24×C5 |
| Frattini | C22 | C23×C5×D5 |
| Fitting | C25×C52 | C2 |
| socle | C23×C52 | C23 |
| hypercenter | C25×C5 | D5 |
| hypocenter | C5 | C2×C5×#120 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C23×C5 ◁ C25×C5 | |
2072 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 2072 conjugacy classes of subgroups — too many to draw. Only its 318 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
460 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13106618 |
| maximal normal subgroup of | C2×#13106618 |
| maximal quotient of | C5×#10615769, C5×#10615835 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9346);