Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C25×#120 ⋊ C2 |
| Sylow | C25 ⋊ B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #11716499 |
| commutator, cosocle | C23×C25 | C23 |
| Frattini | C23×C5 | C22×D5 |
| Fitting | C25×#120 | C2 |
| socle | C2×C5 | #4083 |
| hypercenter | #120 | D25 |
| hypocenter | C25 | B(4,𝔽2) |
| LCS | G ▷ C23×C25 ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #120 | |
297 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 51 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|g^5=h,c^a=ce,d^a=df,g^a=g^4h^4,h^a=h^4,c^b=cd,e^b=ef184 conjugacy classes — view the full character table.
| maximal subgroup of | D25×B(4,𝔽2), #72275793 |
| maximal normal subgroup of | D25×B(4,𝔽2), #72275793 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 659);