Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#87855 |
| derived, Sylow | C52 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #1043 |
| commutator, hypocenter | C52 | C2×C4×C8 |
| Frattini | C22 | C22×#1043 |
| Fitting | C42×C52 | C4 |
| socle | C22×C52 | C22×C4 |
| prime radical | C22×C5⋊D5 | C2×C4 |
| cosocle | C2×#1039 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C42 | |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C8×#1043, C4×#11716860, C8×#87855, … |
| maximal normal subgroup of | C4×C8×#1043, C4×#11716860, C8×#87855, … |
| maximal quotient of | C8×#87855, #72220897, #72242098 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 7039);