Finite Group DatabasebetaFinite Group Databasebeta| order | 528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×Q8×C11 ⋊ C2 |
| Hall | C3×C11 ⋊ #41 |
| Sylow | C11 ⋊ #239 |
| Sylow | C3 ⋊ #4343 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D33 |
| commutator, socle, cosocle | C2×C3×C11 | C23 |
| Fitting | C3×Q8×C11 | C2 |
| hypercenter | Q8 | D33 |
| hypocenter | C3×C11 | #41 |
| LCS | G ▷ C2×C3×C11 ▷ C3×C11 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 264 |
Polycyclic presentation:
2^4,3,11|b^2=d,c^2=d,c^a=cd,e^a=e^2,f^a=f^10,c^b=cd90 conjugacy classes — view the full character table.
| maximal subgroup of | #11760956, #11760962, #11760971, … |
| maximal normal subgroup of | #11760956, #11760962, #11760971, … |
| maximal quotient of | #11761230, #11761232, #11761233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(528, 153);