Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C25 ⋊ C2 |
| Sylow | C25 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D25 |
| commutator, cosocle | C22×C25 | C23 |
| Frattini, socle | C22×C5 | C22×D5 |
| Fitting | C22⋊C4×C25 | C2 |
| hypercenter | C22⋊C4 | D25 |
| hypocenter | C25 | #121 |
| LCS | G ▷ C22×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
141 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=d,f^5=g,c^a=cde,f^a=f^4g^4,g^a=g^4,c^b=ce134 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11716446, #13098814, #13098817, … |
| maximal normal subgroup of | C2×#11716446, #13098814, #13098817, … |
| maximal quotient of | #13097922, #13097927, #13097933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 105);