Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C25 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D25 |
| commutator, hypocenter | C25 | C16 |
| Frattini | C5×C8 | D5 |
| Fitting, cosocle | C8×C25 | C2 |
| socle, prime radical | C2×C5 | #168 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C8 | |
15 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 400 |
A minimal faithful permutation representation — 2 generators on 41 points:
(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,12)(14,20)(17,21)(18,22)(19,24)(23,25)(26,27,28,31,29,32,34,37,30,33,35,38,36,39,40,41);(1,15,25,18,4,7,21,19,10,13,16,14,12,11,20,8,6,5,24,17,3,2,22,23,9)Polycyclic presentation:
2^4,5^2|a^2=b,b^2=c,c^2=d,e^5=f^4,e^a=e^4f,f^a=f^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #11716344, C16×D25, #11716346, … |
| maximal normal subgroup of | #11716344, C16×D25, #11716346, … |
| maximal quotient of | #11716342, C2×#87707, C3×#87707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 1);