Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | #95⋊C9 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #63419 |
| commutator, cosocle, hypocenter | #95⋊C9 | C2 |
| Frattini, socle | C23×C3 | S4 |
| Fitting | C3×#95 | D3 |
| LCS | G ▷ #95⋊C9 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3^2,2^5|b^3=c^2,d^2=fg,e^2=f,b^a=b^2c,c^a=c^2,d^a=e,e^a=d,f^a=fg,d^b=eh,e^b=deg,f^b=gh,g^b=fgh,e^d=eh27 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10588302, #11919940, #11919942, … |
| maximal normal subgroup of | C2×#10588302, #11919940, #11919942, … |
| maximal quotient of | #11919921, #11919922, #11919924, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 184);