Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Sylow | C52 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×C5⋊D5 |
| commutator | C2×C52 | C2×C4 |
| Fitting | C2×C4×C52 | C2 |
| socle, prime radical, cosocle | C22×C52 | C22 |
| hypercenter | C2×C4 | C5⋊D5 |
| hypocenter | C52 | C4⋊C4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 400 |
A minimal faithful permutation representation — 3 generators on 18 points:
(1,2,3,4)(6,8)(14,15,17,18,16);(5,6,7,8)(10,11)(12,13)(15,16)(17,18);(9,10,12,13,11)Polycyclic presentation:
2^4,5^2|a^2=d,b^2=c,b^a=bd,e^a=e^4,f^a=f^4106 conjugacy classes — view the full character table.
| maximal subgroup of | #11716955, #11716957, #11716964, … |
| maximal normal subgroup of | #11716955, #11716957, #11716964, … |
| maximal quotient of | #11716674, #11716675, #11716681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 100);