Finite Group DatabasebetaFinite Group Databasebeta| order | 10048 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×D157 |
| Fitting | H(5,𝔽2)×C157 ⋊ C2 |
| Sylow | C157 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D157 |
| commutator, socle, cosocle | C2×C157 | C25 |
| Fitting | H(5,𝔽2)×C157 | C2 |
| hypercenter | H(5,𝔽2) | D157 |
| hypocenter | C157 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C157 ▷ C157 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
898 conjugacy classes of subgroups.
1360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #453×D157, #455×D157, #34109490, … |
| maximal normal subgroup of | #453×D157, #455×D157, #34109490, … |
| maximal quotient of | #518×D157, #520×D157, #34113340, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10048, 1378);