Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C313 ⋊ C2 |
| Sylow | C313 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D313 |
| commutator, socle | C2×C313 | C22×C4 |
| Fitting | M16×C313 | C2 |
| prime radical | #19097561 | C2 |
| cosocle | C4×C313 | C23 |
| hypercenter | M16 | D313 |
| hypocenter | C313 | #131 |
| LCS | G ▷ C2×C313 ▷ C313 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=d,d^2=e,f^a=f^312,c^b=ce,f^c=f^3121580 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34094266, #34094268, #34094271, … |
| maximal normal subgroup of | #34094266, #34094268, #34094271, … |
| maximal quotient of | #34094109, #34094110, #34094117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 154);