Finite Group DatabasebetaFinite Group Databasebeta| order | 552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C23 ⋊ D4 |
| Sylow | C23 ⋊ #67 |
| Sylow | C3 ⋊ C22⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D23 |
| commutator, Fitting, socle, cosocle | C2×C3×C23 | C22 |
| hypocenter | C3×C23 | D4 |
| LCS | G ▷ C2×C3×C23 ▷ C3×C23 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 276 |
Polycyclic presentation:
2^3,3,23|b^a=bc,e^a=e^22,d^b=d^275 conjugacy classes — view the full character table.
| maximal subgroup of | #11764222, #11764228, #11764229, … |
| maximal normal subgroup of | #11764222, #11764228, #11764229, … |
| maximal quotient of | #11764136, #11764139, #11764140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(552, 8);