Finite Group Databasebeta

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C7×C11×A4×C37 #46803293

order34188
automorphism?
homologyAbelianization (H1) = C3×C7×C11×C37 · Schur multiplier (H2) = C2

Aliases

direct productC7×C11×A4×C37
unambiguous semidirect productC22⋊(C3×C7×C11×C37)
unambiguous semidirect product(C22×C11)⋊(C3×C7×C37)

Splittings

Fitting, socle, HallC22×C7×C11×C37 ⋊ C3
derived, SylowC22 ⋊ C3×C7×C11×C37
HallC22×C11×C37 ⋊ C3×C7
HallC22×C7×C37 ⋊ C3×C11
HallC22×C7×C11 ⋊ C3×C37
HallC22×C37 ⋊ C3×C7×C11
HallC22×C11 ⋊ C3×C7×C37
HallC22×C7 ⋊ C3×C11×C37

Subgroups

subgroupG/H
center, hypercenterC7×C11×C37A4
commutator, cosocle, hypocenterC22C3×C7×C11×C37
FrattiniC1G
Fitting, socleC22×C7×C11×C37C3
LCSG ▷ C22
UCSC1 ◁ C7×C11×C37

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11396

Conjugacy classes & character table

11396 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 165);