Finite Group DatabasebetaFinite Group Databasebeta| order | 100 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = D3×GL(2,𝔽5) (order 2880) · Inn(G) = C1 · Out(G) = D3×GL(2,𝔽5) |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C5 |
| abelian | C22×C52 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 100 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,2)(5,6,7,8,9);(3,4)(10,11,12,13,14)100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(100, 16);