Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×#11716882 |
| derived, Sylow | C52 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #1044 |
| commutator, hypocenter | C52 | C22×C16 |
| Frattini | C4 | C22×#1044 |
| Fitting | C2×C52×C8 | C4 |
| socle | C22×C52 | C2×C8 |
| prime radical | C22×C5⋊D5 | C8 |
| cosocle | #6029 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C8 | |
272 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #72242160, C2×#13099848, C2×#13099850 |
| maximal normal subgroup of | #72242160, C2×#13099848, C2×#13099850 |
| maximal quotient of | #72269151 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7203);