Finite Group DatabasebetaFinite Group Databasebeta| order | 8172 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 21696 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C3 |
| abelian | C32×C4×C227 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2 | C2×C32×C227 |
| socle | C2×C32×C227 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
36 conjugacy classes of subgroups.
8172 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C8×C227, C2×C32×C4×C227, C3×C4×C9×C227, … |
| maximal normal subgroup of | C32×C8×C227, C2×C32×C4×C227, C3×C4×C9×C227, … |
| maximal quotient of | C32×C8×C227, C2×C32×C4×C227, C3×C4×C9×C227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8172, 11);