Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #87721 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C25 ⋊ C2 |
| Sylow | C25 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D25 |
| commutator, cosocle | C4×C25 | C22 |
| Frattini | C4×C5 | C2×D5 |
| Fitting | D4×C25 | C2 |
| socle | C2×C5 | C22⋊D5 |
| hypercenter | D4 | D25 |
| hypocenter | C25 | D8 |
| LCS | G ▷ C4×C25 ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
33 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,14,22,10,17,7,6,25,11,9,16,2,19,24,4,8,15,12,23,13,3,21,5,18,20)(27,30)(28,33)(31,32);(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)(28,30)(29,32)(31,33)Polycyclic presentation:
2^4,5^2|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 | D8×D25, #11716473, #11716476, … |
| maximal normal subgroup of | D8×D25, #11716473, #11716476, … |
| maximal quotient of | #11716355, #11716358, #11716374, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 16);