Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C23×C52 ⋊ C22 |
| Sylow | C52 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D52 |
| commutator, socle, cosocle | C2×C52 | C24 |
| Fitting | C23×C52 | C22 |
| hypercenter | C23 | D52 |
| hypocenter | C52 | H(5,𝔽2) |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C23 | |
386 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 108 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|d^a=de,g^a=g^4,c^b=ce,f^b=f^489 conjugacy classes — view the full character table.
| maximal subgroup of | #13100588, #13100589, #13100590, … |
| maximal normal subgroup of | #13100588, #13100589, #13100590, … |
| maximal quotient of | #13105934, #13105936, #13105969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1154);