Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of Dic50 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C25 ⋊ C2 |
| Sylow | C25 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D25 |
| commutator | C2×C25 | C2×C4 |
| Frattini | C4×C5 | C2×D5 |
| Fitting | C8×C25 | C2 |
| socle | C2×C5 | C4×D5 |
| prime radical | C2×D25 | C4 |
| cosocle | C4×C25 | C22 |
| hypercenter | C8 | D25 |
| hypocenter | C25 | M16 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C4 ◁ C8 | |
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:
(1,21,12,24,9,7,14,5,23,4,16,6,22,18,13,8,2,25,10,20,3,15,19,11,17)(26,27,28,31,29,30,32,33);(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,12)(14,20)(17,21)(18,22)(19,24)(23,25)(27,30)(31,33)Polycyclic presentation:
2^4,5^2|b^2=c,c^2=d,e^5=f^4,b^a=bd,e^a=e^4f,f^a=f^4106 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#87712, #11716464, M16×D25, … |
| maximal normal subgroup of | C2×#87712, #11716464, M16×D25, … |
| maximal quotient of | #11716363, #11716364, #11716368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 6);