Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C5 |
No aliases for this group.
| Fitting | C52×#99 ⋊ C2 |
| Sylow | C52 ⋊ B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11717202 |
| commutator, cosocle | C23×C52 | C23 |
| Frattini | C23 | C22×C5⋊D5 |
| Fitting | C52×#99 | C2 |
| socle | C2×C52 | #120 |
| hypercenter | #99 | C5⋊D5 |
| hypocenter | C52 | B(4,𝔽2) |
| LCS | G ▷ C23×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #99 | |
792 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^6,5^2|c^2=e,c^a=ce,d^a=df,g^a=g^4,h^a=h^4,c^b=cd,e^b=ef,d^c=df148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4956);