Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C317 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D317 |
| commutator, socle | C2×C317 | C22×C4 |
| Fitting, prime radical | #41×C317 | C2 |
| cosocle | C4×C317 | C23 |
| hypercenter | #41 | D317 |
| hypocenter | C317 | #131 |
| LCS | G ▷ C2×C317 ▷ C317 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|a^2=d,d^2=e,f^a=f^316,c^b=ce1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35203337, #35203340, #35203342, … |
| maximal normal subgroup of | #35203337, #35203340, #35203342, … |
| maximal quotient of | #35203179, #35203190, #35203250, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 153);