Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| derived, Sylow | C52 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #1044 |
| commutator, hypocenter | C52 | C2×C8 |
| Frattini | C2 | C2×#1044 |
| Fitting | C4×C52 | C4 |
| socle | C2×C52 | C2×C4 |
| prime radical | C2×C5⋊D5 | C4 |
| cosocle | #1039 | C22 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C4 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,3,5,4)(2,6,8,7)(9,10,13,11,12)(14,15,16,18,17);(1,2,4,7,5,8,3,6)(10,11,12,13)(15,16,17,18)Polycyclic presentation:
2^4,5^2|a^2=c,b^2=d,c^2=d,e^a=e^3,f^a=f^2,e^c=e^4,f^c=f^440 conjugacy classes — view the full character table.
| maximal subgroup of | #11716761, #11716763, #11716765, … |
| maximal normal subgroup of | #11716761, #11716763, #11716765, … |
| maximal quotient of | #11716882, #11716883, C4×#6034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 156);