Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q8×C317 ⋊ C2 |
| Sylow | C317 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D317 |
| commutator, socle, cosocle | C22×C317 | C23 |
| Fitting | C2×Q8×C317 | C2 |
| prime radical | C2×D1268 | C2 |
| hypercenter | C2×Q8 | D317 |
| hypocenter | C317 | #124 |
| LCS | G ▷ C22×C317 ▷ C317 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^316,f^b=f^316,f^c=f^3161594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35203019, #35203396, #35203398, … |
| maximal normal subgroup of | #35203019, #35203396, #35203398, … |
| maximal quotient of | #35203088, #35203113, #35203124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 135);