Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26×C5 |
| direct product | C23×#6034 |
| derived, Sylow | C52 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | #1044 |
| commutator, hypocenter | C52 | C23×C8 |
| Frattini | C2 | C23×#1044 |
| Fitting, socle, prime radical | C24×C52 | C4 |
| cosocle | #1039 | C24 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C24 | |
912 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#87862, C22×#11716895 |
| maximal normal subgroup of | C23×#87862, C22×#11716895 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 10128);