Finite Group DatabasebetaFinite Group Databasebeta| order | 2272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C71 ⋊ C2 |
| Sylow | C71 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D71 |
| commutator, socle | C2×C71 | C22×C4 |
| Fitting | M16×C71 | C2 |
| prime radical | #11765865 | C2 |
| cosocle | C4×C71 | C23 |
| hypercenter | M16 | D71 |
| hypocenter | C71 | #131 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^5,71|a^2=d,d^2=e,f^a=f^70,c^b=ce,f^c=f^70370 conjugacy classes — view the full character table.
| maximal subgroup of | #17986113, #17986115, #17986118, … |
| maximal normal subgroup of | #17986113, #17986115, #17986118, … |
| maximal quotient of | #17985956, #17985957, #17985964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2272, 154);