Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #87721 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C25 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D25 |
| commutator, cosocle | C4×C25 | C22 |
| Frattini | C4×C5 | C2×D5 |
| Fitting | Q8×C25 | C2 |
| socle, prime radical | C2×C5 | C22⋊D5 |
| hypercenter | Q8 | D25 |
| hypocenter | C25 | Q16 |
| LCS | G ▷ C4×C25 ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
27 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 400 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,14,22,10,17,7,6,25,11,9,16,2,19,24,4,8,15,12,23,13,3,21,5,18,20)(26,28,30,36)(27,31,33,40)(29,38,39,35)(32,41,37,34);(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,12)(14,20)(17,21)(18,22)(19,24)(23,25)(26,27,30,33)(28,34,36,41)(29,37,39,32)(31,38,40,35)Polycyclic presentation:
2^4,5^2|a^2=d,b^2=d,c^2=d,e^5=f^4,b^a=bc,c^a=cd,e^a=e^4f,f^a=f^4,c^b=cd67 conjugacy classes — view the full character table.
| maximal subgroup of | #11716477, #11716478, Q16×D25, … |
| maximal normal subgroup of | #11716477, #11716478, Q16×D25, … |
| maximal quotient of | #11716355, #11716357, #11716384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 17);