Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
No aliases for this group.
| Fitting | C2×C52×D4 ⋊ C2 |
| Sylow | C52 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×C5⋊D5 |
| commutator, socle, cosocle | C2×C52 | C24 |
| Fitting | C2×C52×D4 | C2 |
| hypercenter | C2×D4 | C5⋊D5 |
| hypocenter | C52 | H(5,𝔽2) |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^5,5^2|d^a=de,f^a=f^4,g^a=g^4,c^b=ce137 conjugacy classes — view the full character table.
| maximal subgroup of | #13101620, #13101643, #13101700, … |
| maximal normal subgroup of | #13101620, #13101643, #13101700, … |
| maximal quotient of | #13107012, #13107015, #13107019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1176);