Finite Group DatabasebetaFinite Group Databasebeta| order | 200 |
| isoclinism | isoclinic class of D25 |
| automorphism | Aut(G) = C22×AGL(1,ℤ/25) (order 2000) · Inn(G) = D25 · Out(G) = C23×C5 |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C25 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D25 |
| commutator, hypocenter | C25 | C8 |
| Frattini | C4×C5 | D5 |
| Fitting, cosocle | C4×C25 | C2 |
| socle, prime radical | C2×C5 | Dic5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C4 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 2 generators on 33 points:
(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,12)(14,20)(17,21)(18,22)(19,24)(23,25)(26,27,28,30,29,31,32,33);(1,15,25,18,4,7,21,19,10,13,16,14,12,11,20,8,6,5,24,17,3,2,22,23,9)Polycyclic presentation:
2^3,5^2|a^2=b,b^2=c,d^5=e^4,d^a=d^4e,e^a=e^456 conjugacy classes — view the full character table.
| maximal subgroup of | #87709, C8×D25, #87712, … |
| maximal normal subgroup of | #87709, C8×D25, #87712, … |
| maximal quotient of | #87707, C2×#6014, C3×#6014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(200, 1);