Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #6053⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ #336 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | #6053⋊C2 |
| commutator | C5⋊D5 | C4×C8 |
| Fitting, socle | C22×C52 | M16 |
| prime radical | C22×C5⋊D5 | C2×C4 |
| cosocle | C22×#1043 | C22 |
| hypocenter | C52 | #336 |
| LCS | G ▷ C5⋊D5 ▷ C52 | |
| UCS | C1 ◁ C22 | |
199 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=e,b^2=c,c^2=f,b^a=bdf,g^a=g^4,g^b=h,h^b=g^2,g^c=g^2,h^c=h^2,g^f=g^4,h^f=h^452 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5654);