Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×2−1+4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3489 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D79 |
| commutator, socle, cosocle | C22×C79 | C25 |
| Fitting | C2×2−1+4×C79 | C2 |
| hypercenter | C2×2−1+4 | D79 |
| hypocenter | C79 | #3489 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
1522 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^781370 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34319640, #34319651, #34319662, … |
| maximal normal subgroup of | #34319640, #34319651, #34319662, … |
| maximal quotient of | #34448302, #34448572, #34448589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18183);