Finite Group DatabasebetaFinite Group Databasebeta| order | 10432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C163 ⋊ #398 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D163 |
| commutator, socle, prime radical, cosocle | C23×C163 | C23 |
| Fitting | C2×C4⋊C4×C163 | C2 |
| hypercenter | C2×C4⋊C4 | D163 |
| hypocenter | C163 | #398 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
150 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,163|a^2=e,b^2=d,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^1621642 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35212541, #35212543, #35213533, … |
| maximal normal subgroup of | #35212541, #35212543, #35213533, … |
| maximal quotient of | #35212786, #35212789, #35212791, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 479);