Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of #92563 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C52 |
| direct product | C2×#92563 |
| Fitting, socle | C2×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92563 |
| commutator, hypocenter | C53 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C53 | C4 |
| prime radical | C2×C5⋊(C5⋊D5) | C2 |
| cosocle | C5⋊(C5⋊D5) | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2 | |
248 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #14522678, #14522679, #14522680, … |
| maximal normal subgroup of | #14522678, #14522679, #14522680, … |
| maximal quotient of | #14522816, #14522817, C4×#92563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 189);