Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×D4×C313 ⋊ C2 |
| Sylow | C313 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D313 |
| commutator, socle, cosocle | C22×C313 | C23 |
| Fitting | C2×D4×C313 | C2 |
| hypercenter | C2×D4 | D313 |
| hypocenter | C313 | #120 |
| LCS | G ▷ C22×C313 ▷ C313 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|b^a=bd,c^a=ce,f^c=f^3121574 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34093938, #34093940, #34094339, … |
| maximal normal subgroup of | #34093938, #34093940, #34094339, … |
| maximal quotient of | #34094007, #34094023, #34094024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 114);