Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#87748 |
| Fitting | C2×Q8×C25 ⋊ C2 |
| Sylow | C25 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D25 |
| commutator, cosocle | C2×C25 | C24 |
| Frattini | C2×C5 | C23×D5 |
| Fitting | C2×Q8×C25 | C2 |
| socle | C22×C5 | C22×D5 |
| hypercenter | C2×Q8 | D25 |
| hypocenter | C25 | C2×#41 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13098026, #13098079, #13098080, … |
| maximal normal subgroup of | #13098026, #13098079, #13098080, … |
| maximal quotient of | C2×#11716452, C2×#11716454, C2×#11716455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 224);