Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C52 ⋊ C22 |
| Sylow | C52 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D52 |
| commutator, socle, cosocle | C2×C52 | C23 |
| Fitting | C22×C52 | C22 |
| hypercenter | C22 | D52 |
| hypocenter | C52 | C2×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2 ◁ C22 | |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 20 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2)(3,4)(5,6,8,9,7)(10,11,13,14,12);(2,4)(6,7)(8,9);(2,4)(11,12)(13,14)Polycyclic presentation:
2^4,5^2|c^a=cd,f^a=f^4,c^b=cd,e^b=e^446 conjugacy classes — view the full character table.
| maximal subgroup of | #11716796, #11717375, #11717377, … |
| maximal normal subgroup of | #11716796, #11717375, #11717377, … |
| maximal quotient of | #11716958, #11716971, #11716984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 180);