Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C25 ⋊ C2 |
| Sylow | C25 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D25 |
| commutator, cosocle | C4×C25 | C23 |
| Frattini | C4×C5 | C22×D5 |
| Fitting | #41×C25 | C2 |
| socle | C2×C5 | C2×C22⋊D5 |
| hypercenter | #41 | D25 |
| hypocenter | C25 | #135 |
| LCS | G ▷ C4×C25 ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ #41 | |
93 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=e,d^2=e,f^5=g,c^a=cd,d^a=de,f^a=f^4g^4,g^a=g^4,d^c=de134 conjugacy classes — view the full character table.
| maximal subgroup of | #13098098, #13098099, #13098419, … |
| maximal normal subgroup of | #13098098, #13098099, #13098419, … |
| maximal quotient of | #13098271, #13098275, #13098278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 172);