Finite Group DatabasebetaFinite Group Databasebeta| order | 200 |
| isoclinism | isoclinic class of #6045 |
| automorphism | Aut(G) order 96000 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Sylow | C52 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×C5⋊D5 |
| commutator, socle, prime radical, cosocle | C2×C52 | C22 |
| Fitting | C4×C52 | C2 |
| hypercenter | C4 | C5⋊D5 |
| hypocenter | C52 | Q8 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C4 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,3,4,8)(2,5,6,7)(14,15,17,18,16);(1,2,4,6)(3,7,8,5)(10,11)(12,13)(15,16)(17,18);(9,10,12,13,11)Polycyclic presentation:
2^3,5^2|a^2=c,b^2=c,b^a=bc,d^a=d^4,e^a=e^453 conjugacy classes — view the full character table.
| maximal subgroup of | #87773, #87776, #87800, … |
| maximal normal subgroup of | #87773, #87776, #87800, … |
| maximal quotient of | #87806, C4⋊#1039, C2×#6045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(200, 32);