Finite Group DatabasebetaFinite Group Databasebeta| order | 200 |
| isoclinism | isoclinic class of D52 |
| automorphism | Aut(G) = #72275679 (order 3200) · Inn(G) = D52 · Out(G) = #120 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D52 |
| commutator, hypocenter | C52 | C2×C4 |
| Fitting, socle, cosocle | C2×C52 | C22 |
| prime radical | C2×C5⋊D5 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 20 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,3,4,2)(6,7)(8,9)(10,11,13,14,12);(1,2,4,3)(5,6,8,9,7)(11,12)(13,14)Polycyclic presentation:
2^3,5^2|a^2=c,b^2=c,e^a=e^4,d^b=d^432 conjugacy classes — view the full character table.
| maximal subgroup of | #87827, #87829, #87830, … |
| maximal normal subgroup of | #87827, #87829, #87830, … |
| maximal quotient of | #87767, #87769, Dic52, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(200, 23);