Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of D5×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C5 |
| direct product | C2×D5×C5⋊D5 |
| Fitting, socle | C2×C53 ⋊ C22 |
| derived, Sylow | C53 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×C5⋊D5 |
| commutator, cosocle, hypocenter | C53 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C53 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
376 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #14522679, #14522686, #14522693, … |
| maximal normal subgroup of | #14522679, #14522686, #14522693, … |
| maximal quotient of | Dic10×C5⋊D5, #14522863, #14522864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 194);