Finite Group DatabasebetaFinite Group Databasebeta| order | 10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊C4×C317 ⋊ C2 |
| Sylow | C317 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D317 |
| commutator, socle, cosocle | C22×C317 | C23 |
| Fitting | C22⋊C4×C317 | C2 |
| hypercenter | C22⋊C4 | D317 |
| hypocenter | C317 | #120 |
| LCS | G ▷ C22×C317 ▷ C317 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,317|b^a=bd,c^a=ce,f^a=f^316,f^c=f^3161594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35203411, #120×D317, C2×#23778750, … |
| maximal normal subgroup of | #35203411, #120×D317, C2×#23778750, … |
| maximal quotient of | #35203078, #35203097, #35203098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10144, 116);