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) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D52 |
| commutator, Fitting, socle, cosocle | C2×C52 | C22 |
| hypocenter | C52 | D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 14 points:
(2,4)(6,7)(8,9)(10,11,13,14,12);(1,2)(3,4)(5,6,8,9,7)(11,12)(13,14)Polycyclic presentation:
2^3,5^2|b^a=bc,e^a=e^4,d^b=d^429 conjugacy classes — view the full character table.
| maximal subgroup of | #87837, #87838, #87870, … |
| maximal normal subgroup of | #87837, #87838, #87870, … |
| maximal quotient of | #87770, #87772, #87775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(200, 24);