Finite Group DatabasebetaFinite Group Databasebeta| order | 200 |
| isoclinism | isoclinic class of #6037 |
| automorphism | Aut(G) = #72275679 (order 3200) · Inn(G) = D52 · Out(G) = #104 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C52 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D52 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C52 | C22 |
| hypocenter | C52 | Q8 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,3,4,8)(2,5,6,7)(10,11)(12,13)(14,15,17,18,16);(1,2,4,6)(3,7,8,5)(9,10,12,13,11)(15,16)(17,18)Polycyclic presentation:
2^3,5^2|a^2=c,b^2=c,b^a=bc,e^a=e^4,d^b=d^429 conjugacy classes — view the full character table.
| maximal subgroup of | #87838, #87839, D5×Dic10, … |
| maximal normal subgroup of | #87838, #87839, D5×Dic10, … |
| maximal quotient of | #87780, #87781, C2×#6039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(200, 26);