Finite Group DatabasebetaFinite Group Databasebeta| order | 2272 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#11765864 |
| Fitting | C2×D4×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D71 |
| commutator, cosocle | C2×C71 | C24 |
| Frattini | C2 | C23×D71 |
| Fitting | C2×D4×C71 | C2 |
| socle | C22×C71 | C23 |
| hypercenter | C2×D4 | D71 |
| hypocenter | C71 | C2×#41 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1136 |
370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #17985971, #17985980, #17985992, … |
| maximal normal subgroup of | #17985971, #17985980, #17985992, … |
| maximal quotient of | C2×#14556084, C2×#14556086, C2×(C22⋊D71)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2272, 188);