Finite Group DatabasebetaFinite Group Databasebeta| order | 1000 |
| isoclinism | isoclinic class of ((C5⋊D5)⋊C5)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | H(3,𝔽5) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ((C5⋊D5)⋊C5)⋊C2 |
| commutator, hypocenter | H(3,𝔽5) | C2×C4 |
| Frattini, socle | C2×C5 | D52 |
| Fitting, cosocle | C2×H(3,𝔽5) | C22 |
| prime radical | C2×(C5⋊D5)⋊C5 | C2 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
Polycyclic presentation:
2^3,5^3|b^2=c,e^a=e^4,f^a=f^4,d^b=d^4,f^b=f^4,e^d=ef40 conjugacy classes — view the full character table.
| maximal subgroup of | #14522286, #14522287, #14522288, … |
| maximal normal subgroup of | #14522286, #14522287, #14522288, … |
| maximal quotient of | #14522128, #14522129, #14522146, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 43);