Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D4×Q8×D79 |
| Fitting | D4×Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×D4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C25 |
| Fitting | D4×Q8×C79 | C2 |
| prime radical | C2×D4×D79 | C22 |
| hypercenter | D4×Q8 | D79 |
| hypocenter | C79 | C2×D4×Q8 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1568 conjugacy classes of subgroups.
1025 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1627×D79, #1637×D79, #1651×D79, … |
| maximal normal subgroup of | #1627×D79, #1637×D79, #1651×D79, … |
| maximal quotient of | Q8×C22⋊C4×D79, D4×C4⋊C4×D79, Q8×C4⋊C4×D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17980);