Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×Dic317 |
| Sylow | C317 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D317 |
| commutator | C2×C317 | C22×C4 |
| Fitting | C2×Q8×C317 | C2 |
| socle, prime radical, cosocle | C22×C317 | C23 |
| hypercenter | C2×Q8 | D317 |
| hypocenter | C317 | C4×Q8 |
| LCS | G ▷ C2×C317 ▷ C317 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
70 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35203308, SD16×Dic317, #35203315, … |
| maximal normal subgroup of | #35203308, SD16×Dic317, #35203315, … |
| maximal quotient of | C4⋊C4×Dic317, #35203109, #35203122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 113);