Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #6037 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C52 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D52 |
| commutator | C2×C52 | C2×C4 |
| Fitting, socle, prime radical, cosocle | C22×C52 | C22 |
| hypocenter | C52 | C4⋊C4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,3,4)(6,8)(10,11)(12,13)(14,15,17,18,16);(5,6,7,8)(9,10,12,13,11)(15,16)(17,18)Polycyclic presentation:
2^4,5^2|a^2=d,b^2=c,b^a=bd,f^a=f^4,e^b=e^458 conjugacy classes — view the full character table.
| maximal subgroup of | #11716954, #11716955, #11716957, … |
| maximal normal subgroup of | #11716954, #11716955, #11716957, … |
| maximal quotient of | #11716612, #11716614, #11716616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 74);