Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24×C4 |
| direct product | C5×#65926 |
| Fitting | C52×#120 ⋊ C2 |
| Sylow | C52 ⋊ #535 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C5 | C23×D5 |
| commutator, cosocle | C22×C5 | C24×C5 |
| Frattini | C22 | C23×C5×D5 |
| Fitting | C52×#120 | C2 |
| socle | C22×C52 | C24 |
| hypercenter | C5×#120 | D5 |
| hypocenter | C5 | C5×#535 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22×C5 ◁ C5×#120 | |
798 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
250 conjugacy classes — view the full character table.
| maximal subgroup of | #72221649, C5×#10604464, #72221706 |
| maximal normal subgroup of | #72221649, C5×#10604464, #72221706 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 9093);