Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of #6953 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#92525 |
| derived, Sylow | H(3,𝔽5) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C5 | C5⋊D5 |
| commutator, hypocenter | H(3,𝔽5) | C2×C4 |
| Frattini | C2×C5 | C2×C5⋊D5 |
| Fitting, prime radical | C22×H(3,𝔽5) | C2 |
| cosocle | C2×H(3,𝔽5) | C22 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C22×C5 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #14522146, #14522147, #14522148, … |
| maximal normal subgroup of | #14522146, #14522147, #14522148, … |
| maximal quotient of | C2×#11758635, #14522232, C4×#92525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 75);