Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #92562 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×#92562 |
| Fitting, socle | C22×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92562 |
| commutator, hypocenter | C53 | C22×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C53 | C4 |
| prime radical | C22×C5⋊(C5⋊D5) | C2 |
| cosocle | C5⋊(C5⋊D5) | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22 | |
1728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 500 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D5⋊#1043, #72259607 |
| maximal normal subgroup of | C22×D5⋊#1043, #72259607 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 952);