Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C52×C16 ⋊ C4 |
| Sylow | C52 ⋊ #346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C2×#1043 |
| commutator, socle | C2×C52 | C4×C8 |
| Fitting | C52×C16 | C4 |
| prime radical | C2×C5⋊D5 | C2×C8 |
| cosocle | C8×C5⋊D5 | C22 |
| hypercenter | C16 | #1043 |
| hypocenter | C52 | #346 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C8 ◁ C16 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^2,h^a=h^2,g^c=g^4,h^c=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13100222, M32×#1043, #72242333, … |
| maximal normal subgroup of | C2×#13100222, M32×#1043, #72242333, … |
| maximal quotient of | C2×#13100222 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2574);