Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×#6032 |
| derived, Sylow | C52 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #1042 |
| commutator, hypocenter | C52 | C22×C8 |
| Frattini | C2 | C22×#1042 |
| Fitting, socle, prime radical | C23×C52 | C4 |
| cosocle | C5×Dic5 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C23 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #13099832, #13100202, C2×Dic5×#170, … |
| maximal normal subgroup of | #13099832, #13100202, C2×Dic5×#170, … |
| maximal quotient of | C22×#87763, C2×#11716841, C2×C4×#6032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1089);