Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #87800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Fitting | C52×C8 ⋊ C2 |
| Sylow | C52 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C4⋊(C5⋊D5) |
| commutator, cosocle | C4×C52 | C22 |
| Frattini | C4 | C2×C5⋊D5 |
| Fitting | C52×C8 | C2 |
| socle | C2×C52 | D4 |
| hypercenter | C8 | C5⋊D5 |
| hypocenter | C52 | D8 |
| LCS | G ▷ C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,6,8,4,7,3,5)(14,15,17,18,16);(2,5)(3,6)(7,8)(10,11)(12,13)(15,16)(17,18);(9,10,12,13,11)Polycyclic presentation:
2^4,5^2|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^4,f^a=f^4103 conjugacy classes — view the full character table.
| maximal subgroup of | #11716587, #11716590, #11716666, … |
| maximal normal subgroup of | #11716587, #11716590, #11716666, … |
| maximal quotient of | #11716666, #11716667, #11716668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 95);