Finite Group DatabasebetaFinite Group Databasebeta| order | 2272 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C71 ⋊ C2 |
| Sylow | C71 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D71 |
| commutator, socle, cosocle | C2×C71 | C24 |
| Fitting | C2×Q8×C71 | C2 |
| hypercenter | C2×Q8 | D71 |
| hypocenter | C71 | 2−1+4 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
Polycyclic presentation:
2^5,71|b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,f^b=f^70,f^d=f^70367 conjugacy classes — view the full character table.
| maximal subgroup of | #17986171, #17986174, #17986181, … |
| maximal normal subgroup of | #17986171, #17986174, #17986181, … |
| maximal quotient of | #17986475, #17986477, #17986480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2272, 194);