Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C32 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C23 | D32 |
| commutator | C2×C32 | C42 |
| Fitting, socle, prime radical, cosocle | C23×C32 | C22 |
| hypocenter | C32 | #95 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C23 | |
179 conjugacy classes of subgroups.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 18 points:
(5,6,7,8)(10,12)(14,15)(16,17,18);(1,2,3,4)(9,10)(11,12)(13,14,15)(17,18)Polycyclic presentation:
2^5,3^2|a^2=d,b^2=c,b^a=be,g^a=g^2,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | #10590071, #10590072, #10591191, … |
| maximal normal subgroup of | #10590071, #10590072, #10591191, … |
| maximal quotient of | #10589155, #10589156, #10589157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 227);