Finite Group DatabasebetaFinite Group Databasebeta| order | 14032 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C877 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#16812881 |
| commutator, socle | C2×C877 | C2×C4 |
| Fitting, prime radical | C22×C877 | C4 |
| cosocle | Dic877 | C22 |
| hypercenter | C22 | #16812881 |
| hypocenter | C877 | M16 |
| LCS | G ▷ C2×C877 ▷ C877 | |
| UCS | C1 ◁ C2 ◁ C22 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7016 |
Polycyclic presentation:
2^4,877|a^2=c,c^2=d,b^a=bd,e^a=e^151,e^c=e^876886 conjugacy classes — view the full character table.
| maximal subgroup of | #43242857, #43242858, C2×#28380522, … |
| maximal normal subgroup of | #43242857, #43242858, C2×#28380522, … |
| maximal quotient of | #43242852, C22⋊#20296271, #43242864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14032, 49);