Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C22 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #64188 |
| commutator, cosocle, hypocenter | #63703 | C2 |
| Frattini, socle | C2×C3 | #1020 |
| Fitting, prime radical | C3×H(5,𝔽2) | D3 |
| LCS | G ▷ #63703 | |
| UCS | C1 ◁ C2 | |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2,3^2,2^5|a^2=h,b^3=c,f^2=h,g^2=h,b^a=b^2c^2,c^a=c^2,d^a=e,e^a=d,f^a=gh,g^a=fh,d^b=e,e^b=de,f^b=fg,g^b=f,f^d=fh,g^e=gh,g^f=gh24 conjugacy classes — view the full character table.
| maximal subgroup of | #11919980, #11919982, #11919984, … |
| maximal normal subgroup of | #11919980, #11919982, #11919984, … |
| maximal quotient of | #11920447, #11920448, #11920451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4990);