Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×#124×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3561 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C25 |
| Fitting | C2×#124×C79 | C2 |
| hypercenter | C2×#124 | D79 |
| hypocenter | C79 | #3561 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×#124 | |
1032 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,d^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^78,c^b=cg,d^b=df,h^b=h^781130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34180573, #34180577, #34180734, … |
| maximal normal subgroup of | #34180573, #34180577, #34180734, … |
| maximal quotient of | #34451212, #34451280, #34451527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 19082);