Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C2×C79⋊C64 |
| unambiguous semidirect product | (C2×C79)⋊C64 |
| derived, Sylow | C79 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D79 |
| commutator, hypocenter | C79 | C2×C64 |
| Frattini | C32 | C2×D79 |
| Fitting | C2×C32×C79 | C2 |
| socle, prime radical | C22×C79 | C32 |
| cosocle | C32×C79 | C22 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C2×C32 | |
40 conjugacy classes of subgroups.
2624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×Dic79, C4×C79⋊C64, #34176073, … |
| maximal normal subgroup of | C64×Dic79, C4×C79⋊C64, #34176073, … |
| maximal quotient of | C4×C79⋊C64, C22⋊(C79⋊C64), C4⋊(C79⋊C64), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2719);