Finite Group DatabasebetaFinite Group Databasebeta| order | 17872 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C1117 ⋊ C2 |
| Sylow | C1117 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D1117 |
| commutator, cosocle | C4×C1117 | C22 |
| Frattini | C4 | C2×D1117 |
| Fitting | D4×C1117 | C2 |
| socle | C2×C1117 | D4 |
| hypercenter | D4 | D1117 |
| hypocenter | C1117 | D8 |
| LCS | G ▷ C4×C1117 ▷ C2×C1117 ▷ C1117 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8936 |
Polycyclic presentation:
2^4,1117|c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^11162797 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8×D1117, C2×#31821895, #49088552, … |
| maximal normal subgroup of | D8×D1117, C2×#31821895, #49088552, … |
| maximal quotient of | #49088452, #49088453, #49088465, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17872, 25);