Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of #92537⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | H(3,𝔽5) ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92537⋊C2 |
| commutator, hypocenter | H(3,𝔽5) | C42 |
| Frattini, socle | C2×C5 | D5⋊AGL(1,𝔽5) |
| Fitting | C2×H(3,𝔽5) | C2×C4 |
| prime radical, cosocle | C2×#6953 | C22 |
| LCS | G ▷ H(3,𝔽5) | |
| UCS | C1 ◁ C2 | |
137 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,e^a=e^2,f^a=f^2,g^a=g^4,e^b=e^4,g^b=g^4,e^c=e^4,f^c=f^4,f^e=fg44 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#92537⋊C2 |
| maximal normal subgroup of | C4×#92537⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 265);