Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of #92535 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×#92535 |
| Fitting | C2×H(3,𝔽5) ⋊ C4 |
| derived, Sylow | H(3,𝔽5) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92535 |
| commutator, hypocenter | H(3,𝔽5) | C2×C4 |
| Frattini | C5 | C2×#1042 |
| Fitting | C2×H(3,𝔽5) | C4 |
| socle | C2×C5 | #1042 |
| prime radical | C2×(C5⋊D5)⋊C5 | C2 |
| cosocle | (C5⋊D5)⋊C5 | C22 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 50 |
28 conjugacy classes — view the full character table.
| maximal subgroup of | #14522288, #14522289, #14522292, … |
| maximal normal subgroup of | #14522288, #14522289, #14522292, … |
| maximal quotient of | #14522347, #14522348, C4×#92535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 100);