Finite Group DatabasebetaFinite Group Databasebeta| order | 16 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = A8 (order 20160) · Inn(G) = C1 · Out(G) = A8 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C24 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C1 | |
67 conjugacy classes of subgroups.
| minimal degree | μ(G) = 8 |
| transitive degree | μt(G) = 16 |
A minimal faithful permutation representation — 4 generators on 8 points:
(1,2);(3,4);(5,6);(7,8)16 conjugacy classes — view the full character table.
| center of | C2×#95, C22×C22⋊C4, C22×C4⋊C4, … |
| derived subgroup of | C22⋊A4, C24⋊C5, #120⋊C3, … |
| Frattini subgroup of | #342, C4×#95, C22⋊#95, … |
| Fitting subgroup of | C22×A4, C22⋊A4, C24⋊C5, … |
| socle of | C23×C4, C22×A4, C22⋊A4, … |
| maximal subgroup of | C2×C22⋊C4, #120, C23×C4, … |
| maximal normal subgroup of | C2×C22⋊C4, #120, C23×C4, … |
| maximal quotient of | C23×C4, C22×D4, C22×Q8, … |
| outer automorphism group of | #121, C22⋊Q8, D4⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16, 14);