Finite Group DatabasebetaFinite Group Databasebeta| order | 2272 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C71 ⋊ C2 |
| Sylow | C71 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D71 |
| commutator, socle, cosocle | C2×C71 | C24 |
| Fitting | #41×C71 | C2 |
| hypercenter | #41 | D71 |
| hypocenter | C71 | H(5,𝔽2) |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 568 |
Polycyclic presentation:
2^5,71|b^a=be,d^a=de,c^b=ce,f^c=f^70,f^d=f^70367 conjugacy classes — view the full character table.
| maximal subgroup of | #17986165, #17986168, #17986175, … |
| maximal normal subgroup of | #17986165, #17986168, #17986175, … |
| maximal quotient of | #17986471, #17986473, #17986479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2272, 192);