Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | GO+(4,𝔽2) |
| commutator | C3⋊D3 | C42 |
| Fitting, socle | C22×C32 | D4 |
| prime radical, cosocle | C22×C3⋊D3 | C22 |
| hypocenter | C32 | #95 |
| LCS | G ▷ C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C22 | |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,3)(2,5,6)(11,12,13,14);(1,2)(3,6)(4,5)(7,8,9,10)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=d,b^a=bc,f^a=f^2,f^b=g,g^b=f,f^c=f^2,g^c=g^236 conjugacy classes — view the full character table.
| maximal subgroup of | #10593165, #10593338, #10593339, … |
| maximal normal subgroup of | #10593165, #10593338, #10593339, … |
| maximal quotient of | #10590043, #10590044, #10590045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 385);