Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | 2−1+4×C139 ⋊ C2 |
| Sylow | C139 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D139 |
| commutator, socle | C2×C139 | C25 |
| Fitting | 2−1+4×C139 | C2 |
| hypercenter | 2−1+4 | D139 |
| hypocenter | C139 | #585 |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
810 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,139|e^2=f,b^a=bf,d^a=df,c^b=cf,g^c=g^138,g^d=g^138,g^e=g^1381207 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31815751, #31815756, #31815774, … |
| maximal normal subgroup of | #31815751, #31815756, #31815774, … |
| maximal quotient of | #31819604, #31819606, #31819610, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 1386);