Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C11 ⋊ M16 |
| Sylow | C11 ⋊ ΓL(1,𝔽25) |
| Sylow | C3 ⋊ #4318 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D3×D11 |
| commutator, socle | C2×C3×C11 | C2×C4 |
| Fitting, cosocle | C3×C4×C11 | C22 |
| prime radical | C2×D3×C11 | C4 |
| hypocenter | C3×C11 | M16 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C4 | |
40 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=bd,f^a=f^10,e^b=e^278 conjugacy classes — view the full character table.
| maximal subgroup of | D11×ΓL(1,𝔽25), #11760696, #11760715, … |
| maximal normal subgroup of | D11×ΓL(1,𝔽25), #11760696, #11760715, … |
| maximal quotient of | #11760490, (C2×D3)⋊(C11⋊C8), Dic3⋊(C11⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 9);