Finite Group DatabasebetaFinite Group Databasebeta| order | 10780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | C7⋊D7×D55 |
| Fitting, socle, derived, Hall | C5×C72×C11 ⋊ C22 |
| Hall | C72×C11 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D11 |
| Hall | C5×C11 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C2×D55 |
| Sylow | C11 ⋊ D5×C7⋊D7 |
| Sylow | C5 ⋊ D11×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C11 | C22 |
| LCS | G ▷ C5×C72×C11 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
754 conjugacy classes — view the full character table.
| maximal subgroup of | D55×ΓL(1,𝔽8)⋊D7, D55×#64424, D55×#64425, … |
| maximal normal subgroup of | D55×ΓL(1,𝔽8)⋊D7, D55×#64424, D55×#64425, … |
| maximal quotient of | C3×C7⋊D7×D55, C7⋊D7×D165, D55×C3⋊(C7⋊D7), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10780, 92);