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; only the 63 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,163|a^2=e,b^2=d,c^2=d,b^a=bd,c^a=ce,g^a=g^162,c^b=cf1642 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #398×D163, C2×#23781598, #35217778, … |
| maximal normal subgroup of | #398×D163, C2×#23781598, #35217778, … |
| maximal quotient of | #35212788, #35212789, #35212790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10432, 482);