Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C64×C79 ⋊ C2 |
| Sylow | C79 ⋊ SD128 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D2528 |
| commutator, cosocle | C32×C79 | C22 |
| Frattini | C32 | C2×D79 |
| Fitting | C64×C79 | C2 |
| socle | C2×C79 | D32 |
| prime radical | D2528 | C2 |
| hypercenter | C64 | D79 |
| hypocenter | C79 | SD128 |
| LCS | G ▷ C32×C79 ▷ C16×C79 ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ C64 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,h^a=h^78,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^782531 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD128×D79, C2×#23761616, #34209322, … |
| maximal normal subgroup of | SD128×D79, C2×#23761616, #34209322, … |
| maximal quotient of | #34176148, #34176151, #34176171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2726);