Finite Group DatabasebetaFinite Group Databasebeta| order | 14176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20296786 |
| Fitting | C2×D4×C443 ⋊ C2 |
| Sylow | C443 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D443 |
| commutator, cosocle | C2×C443 | C24 |
| Frattini | C2 | C23×D443 |
| Fitting | C2×D4×C443 | C2 |
| socle | C22×C443 | C23 |
| hypercenter | C2×D4 | D443 |
| hypocenter | C443 | C2×#41 |
| LCS | G ▷ C2×C443 ▷ C443 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7088 |
2230 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43247689, #43247698, #43247710, … |
| maximal normal subgroup of | #43247689, #43247698, #43247710, … |
| maximal quotient of | C2×#28381842, C2×#28381844, C2×(C22⋊D443)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14176, 188);