Finite Group Databasebeta

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D7×D1221 #46803282

order34188
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD7×D1221
unambiguous semidirect product(C3×D7)⋊D407
unambiguous semidirect product(C11×D7)⋊D111
unambiguous semidirect product(D7×C37)⋊D33

Splittings

Fitting, socle, derived, HallC3×C7×C11×C37 ⋊ C22
HallC7×C11×C37 ⋊ C2×D3
HallC3×C11×C37 ⋊ C2×D7
HallC3×C7×C37 ⋊ C2×D11
HallC11×C37 ⋊ D3×D7
HallC7×C37 ⋊ C2×D33
HallC3×C7×C11 ⋊ C2×D37
HallC3×C37 ⋊ D7×D11
HallC7×C11 ⋊ C2×D111
SylowC37 ⋊ D7×D33
HallC3×C11 ⋊ D7×D37
HallC3×C7 ⋊ C2×D407
SylowC11 ⋊ D7×D111
SylowC7 ⋊ C2×D1221
SylowC3 ⋊ D7×D407

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C37C22
LCSG ▷ C3×C7×C11×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

3060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 154);