Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C11 ⋊ D8 |
| Sylow | C11 ⋊ D24 |
| Sylow | C3 ⋊ #4323 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #63142 |
| commutator, Fitting, cosocle | C3×C4×C11 | C22 |
| Frattini, hypercenter | C4 | D3×D11 |
| socle | C2×C3×C11 | D4 |
| hypocenter | C3×C11 | D8 |
| LCS | G ▷ C3×C4×C11 ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2 ◁ C4 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3,11|a^2=c,c^2=d,b^a=bc,f^a=f^10,c^b=cd,e^b=e^260 conjugacy classes — view the full character table.
| maximal subgroup of | D11×D24, #11760699, #11760700, … |
| maximal normal subgroup of | D11×D24, #11760699, #11760700, … |
| maximal quotient of | #11760476, #11760481, #11760482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 13);