Finite Group DatabasebetaFinite Group Databasebeta| order | 2272 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C71 ⋊ C2 |
| Sylow | C71 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D71 |
| commutator, socle, cosocle | C2×C71 | C24 |
| Fitting | C2×D4×C71 | C2 |
| hypercenter | C2×D4 | D71 |
| hypocenter | C71 | H(5,𝔽2) |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
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^d=f^70367 conjugacy classes — view the full character table.
| maximal subgroup of | #17986166, #17986169, #17986176, … |
| maximal normal subgroup of | #17986166, #17986169, #17986176, … |
| maximal quotient of | #17986471, #17986472, #17986474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2272, 191);