Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C52×D4 ⋊ C22 |
| Sylow | C52 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D52 |
| commutator, socle, cosocle | C2×C52 | C24 |
| Fitting | C52×D4 | C22 |
| hypercenter | D4 | D52 |
| hypocenter | C52 | C2×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ D4 | |
382 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|c^2=e,d^a=de,g^a=g^4,d^b=de,f^b=f^4,d^c=de80 conjugacy classes — view the full character table.
| maximal subgroup of | #13103716, #13103729, #13104053, … |
| maximal normal subgroup of | #13103716, #13103729, #13104053, … |
| maximal quotient of | #13105116, #13105120, #13105124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1136);