Finite Group DatabasebetaFinite Group Databasebeta| order | 2272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×Q8×C71 ⋊ C2 |
| Sylow | C71 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D71 |
| commutator, socle, cosocle | C22×C71 | C23 |
| Fitting | C2×Q8×C71 | C2 |
| prime radical | C22×D71 | C22 |
| hypercenter | C2×Q8 | D71 |
| hypocenter | C71 | C22⋊Q8 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^5,71|a^2=d,b^2=d,b^a=bd,c^a=ce,f^c=f^70364 conjugacy classes — view the full character table.
| maximal subgroup of | #17986148, #17986153, #17986158, … |
| maximal normal subgroup of | #17986148, #17986153, #17986158, … |
| maximal quotient of | #17985856, #17985870, #17985880, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2272, 122);