Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C5 |
No aliases for this group.
| Fitting | C52×#120 ⋊ C2 |
| Sylow | C52 ⋊ #546 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×#120 | C2 |
| hypercenter | #120 | C5⋊D5 |
| hypocenter | C52 | #546 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #120 | |
1336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|d^2=f,b^a=bf,g^a=g^4,h^a=h^4,d^b=df,d^c=de193 conjugacy classes — view the full character table.
| maximal subgroup of | #72221186, #72221188, C5⋊D5×#546 |
| maximal normal subgroup of | #72221186, #72221188, C5⋊D5×#546 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9472);