Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #64945 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#65512 |
| Fitting | C22×C52×D4 ⋊ C2 |
| Sylow | C52 ⋊ #392 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C5 | C22×D5 |
| commutator, cosocle | C23×C5 | C23×C5 |
| Frattini | C23 | C22×C5×D5 |
| Fitting | C22×C52×D4 | C2 |
| socle | C23×C52 | C23 |
| hypercenter | C22×C5×D4 | D5 |
| hypocenter | C5 | C5×#392 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23×C5 ◁ C22×C5×D4 | |
880 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
310 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72223346 |
| maximal normal subgroup of | #72223346 |
| maximal quotient of | C5×#10602562, C5×#10602508, C5×#10602651 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4836);