Finite Group DatabasebetaFinite Group Databasebeta| order | 2224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D4×D139 |
| Fitting | D4×C139 ⋊ C2 |
| Sylow | C139 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D139 |
| commutator, socle, cosocle | C2×C139 | C23 |
| Fitting | D4×C139 | C2 |
| hypercenter | D4 | D139 |
| hypocenter | C139 | C2×D4 |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C2 ◁ D4 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 556 |
355 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8×D139, SD16×D139, #17984866, … |
| maximal normal subgroup of | D8×D139, SD16×D139, #17984866, … |
| maximal quotient of | C22⋊C4×D139, C4⋊C4×D139, (C22⋊D139)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2224, 34);