Finite Group DatabasebetaFinite Group Databasebeta| order | 200 |
| isoclinism | isoclinic class of #1044 |
| automorphism | Aut(G) = C2×AGL(1,𝔽5)2⋊C2 (order 1600) · Inn(G) = #1044 · Out(G) = C22×C4 |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C5 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #1044 |
| commutator, hypocenter | C52 | C8 |
| Fitting, socle, prime radical | C2×C52 | C4 |
| cosocle | #1039 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,3,5,4,6,7,8)(10,11,12,13)(15,16,17,18);(9,10,13,11,12)(14,15,16,18,17)Polycyclic presentation:
2^3,5^2|a^2=b,b^2=c,d^a=d^3,e^a=e^2,d^b=d^4,e^b=e^420 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#170, #87834, #87837, … |
| maximal normal subgroup of | D5⋊#170, #87834, #87837, … |
| maximal quotient of | #87765, C2×#6034, C3×#6034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(200, 21);