Finite Group DatabasebetaFinite Group Databasebeta| order | 400 |
| isoclinism | isoclinic class of #6045 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C2×C4×C52 ⋊ C2 |
| Sylow | C52 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×C5⋊D5 |
| commutator, socle, cosocle | C2×C52 | C23 |
| Frattini | C2 | C22×C5⋊D5 |
| Fitting | C2×C4×C52 | C2 |
| hypercenter | C2×C4 | C5⋊D5 |
| hypocenter | C52 | #41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
160 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 200 |
A minimal faithful permutation representation — 3 generators on 18 points:
(2,6)(5,8)(14,15,17,18,16);(1,3,4,7)(2,5,6,8)(9,10,12,13,11);(1,2)(3,5)(4,6)(7,8)(10,11)(12,13)(15,16)(17,18)Polycyclic presentation:
2^4,5^2|b^2=d,c^a=cd,e^a=e^4,f^a=f^4106 conjugacy classes — view the full character table.
| maximal subgroup of | #11716611, #11716672, #11716692, … |
| maximal normal subgroup of | #11716611, #11716672, #11716692, … |
| maximal quotient of | C4×#6045, #11717190, #11717192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(400, 194);