Finite Group DatabasebetaFinite Group Databasebeta| order | 200 |
| isoclinism | isoclinic class of #1043 |
| automorphism | Aut(G) = C2×AGL(2,𝔽5) (order 24000) · Inn(G) = #1043 · Out(G) = C2×S5 |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #1043 |
| commutator, hypocenter | C52 | C8 |
| Fitting, socle, prime radical | C2×C52 | C4 |
| cosocle | #1039 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,3,5,4,6,7,8)(10,11,12,13)(15,16,17,18);(14,15,16,18,17);(9,10,11,13,12)Polycyclic presentation:
2^3,5^2|a^2=b,b^2=c,d^a=d^2,e^a=e^2,d^b=d^4,e^b=e^420 conjugacy classes — view the full character table.
| maximal subgroup of | #87822, D5⋊#170, #87834, … |
| maximal normal subgroup of | #87822, D5⋊#170, #87834, … |
| maximal quotient of | #87764, C2×#6033, C3×#6033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(200, 20);