Finite Group DatabasebetaFinite Group Databasebeta| order | 14176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C443 ⋊ C2 |
| Sylow | C443 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D443 |
| commutator, socle | C2×C443 | C22×C4 |
| Fitting | M16×C443 | C2 |
| prime radical | #20296787 | C2 |
| cosocle | C4×C443 | C23 |
| hypercenter | M16 | D443 |
| hypocenter | C443 | #131 |
| LCS | G ▷ C2×C443 ▷ C443 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7088 |
Polycyclic presentation:
2^5,443|a^2=d,d^2=e,f^a=f^442,c^b=ce,f^c=f^4422230 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43247831, #43247833, #43247836, … |
| maximal normal subgroup of | #43247831, #43247833, #43247836, … |
| maximal quotient of | #43247674, #43247675, #43247682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14176, 154);