Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×C79⋊C32 |
| derived, Sylow | C79 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D79 |
| commutator, hypocenter | C79 | C4×C32 |
| Frattini | C2×C16 | C2×D79 |
| Fitting | C4×C16×C79 | C2 |
| socle, prime radical | C22×C79 | C2×C16 |
| cosocle | C2×C16×C79 | C22 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C4×C16 | |
72 conjugacy classes of subgroups.
2624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C79⋊C8, C8×C79⋊C32, #34175596, … |
| maximal normal subgroup of | C32×C79⋊C8, C8×C79⋊C32, #34175596, … |
| maximal quotient of | C8×C79⋊C32, #34175600, #34175956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2642);