Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C2 | #10596770 |
| commutator, prime radical, hypocenter | Ω+(4,𝔽3) | C4 |
| Fitting | H(5,𝔽2) | #157 |
| cosocle | #10596399 | C2 |
| LCS | G ▷ Ω+(4,𝔽3) | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 96 |
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^2,3^2,2^5|a^2=b,b^2=i,e^2=i,f^2=i,g^2=i,h^2=i,c^a=d^2,d^a=c,e^a=g,f^a=h,g^a=ef,h^a=fi,c^b=c^2,d^b=d^2,e^b=ef,f^b=fi,g^b=gh,h^b=hi,e^c=f,f^c=efi,g^d=ghi,h^d=g,f^e=fi,h^g=hi19 conjugacy classes — view the full character table.
| maximal subgroup of | #72209932 |
| maximal normal subgroup of | #72209932 |
| maximal quotient of | #72227890 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157451);