Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #87735 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C25 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#1035 |
| commutator | C2×C25 | C2×C4 |
| Frattini, socle | C2×C5 | C2×AGL(1,𝔽5) |
| Fitting | C4×C25 | C4 |
| prime radical | C2×D25 | C4 |
| cosocle | Dic25 | C22 |
| hypercenter | C4 | #1035 |
| hypocenter | C25 | M16 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C2 ◁ C4 | |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,7,12,10,5,3,19,17,15,13,8,25,24,16,22,20,21,6,11,14,9,2,4,23,18)(26,28,30,29)(27,31,32,33);(2,4,5,10)(3,8,9,20)(6,14,15,19)(7,17,18,11)(12,22,23,25)(13,16,21,24)(26,27,29,31,30,32,28,33)Polycyclic presentation:
2^4,5^2|a^2=c,b^2=d,c^2=d,e^5=f,b^a=bd,e^a=e^2f,f^a=f^2,e^c=e^4f^4,f^c=f^434 conjugacy classes — view the full character table.
| maximal subgroup of | #11716407, #11716408, #11716423, … |
| maximal normal subgroup of | #11716407, #11716408, #11716423, … |
| maximal quotient of | C4⋊#6016, #11716417, #11716418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 29);