Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C25 ⋊ C2 |
| Sylow | C25 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D25 |
| commutator, cosocle | C2×C25 | C23 |
| Frattini, socle | C2×C5 | C22×D5 |
| Fitting | D4×C25 | C2 |
| hypercenter | D4 | D25 |
| hypocenter | C25 | #41 |
| LCS | G ▷ C2×C25 ▷ C25 | |
| UCS | C1 ◁ C2 ◁ D4 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 3 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)(27,31)(28,32);(26,28,29,32)(27,30,31,33);(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,12)(14,20)(17,21)(18,22)(19,24)(23,25)(26,27)(28,30)(29,31)(32,33)Polycyclic presentation:
2^4,5^2|b^2=d,e^5=f^4,c^a=cd,e^a=e^4f,f^a=f^4,c^b=cd70 conjugacy classes — view the full character table.
| maximal subgroup of | #11716423, #11716473, #11716474, … |
| maximal normal subgroup of | #11716423, #11716473, #11716474, … |
| maximal quotient of | #11716439, #11716440, #11716441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 40);