Finite Group DatabasebetaFinite Group Databasebeta| order | 17872 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D1117 |
| Fitting | Q8×C1117 ⋊ C2 |
| Sylow | C1117 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D1117 |
| commutator, socle, cosocle | C2×C1117 | C23 |
| Fitting | Q8×C1117 | C2 |
| prime radical | C2×D1117 | C22 |
| hypercenter | Q8 | D1117 |
| hypocenter | C1117 | C2×Q8 |
| LCS | G ▷ C2×C1117 ▷ C1117 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8936 |
2800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD16×D1117, Q16×D1117, #49088561, … |
| maximal normal subgroup of | SD16×D1117, Q16×D1117, #49088561, … |
| maximal quotient of | C4⋊C4×D1117, #49088497, Q8×Dic1117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17872, 37);