Finite Group Databasebeta

← Prev (#49181233) Next (#49181235) →

C2×C41×D231 #49181234

order37884
automorphism?
homologyAbelianization (H1) = C22×C41 · Schur multiplier (H2) = C2

Aliases

direct productC2×C41×D231
unambiguous semidirect product(C2×C3)⋊(C41×D77)
unambiguous semidirect product(C2×C7)⋊(C41×D33)
unambiguous semidirect product(C2×C11)⋊(C41×D21)

Splittings

Fitting, socleC2×C3×C7×C11×C41 ⋊ C2
derived, HallC3×C7×C11 ⋊ C22×C41
HallC3×C7×C11×C41 ⋊ C22
HallC7×C11×C41 ⋊ C2×D3
HallC3×C11×C41 ⋊ C2×D7
HallC3×C7×C41 ⋊ C2×D11
HallC11×C41 ⋊ C2×D21
HallC7×C41 ⋊ C2×D33
HallC3×C41 ⋊ C2×D77
HallC7×C11 ⋊ C2×D3×C41
HallC3×C11 ⋊ C2×D7×C41
HallC3×C7 ⋊ C2×D11×C41
SylowC11 ⋊ C2×C41×D21
SylowC7 ⋊ C2×C41×D33
SylowC3 ⋊ C2×C41×D77

Subgroups

subgroupG/H
center, hypercenterC2×C41D231
commutator, cosocle, hypocenterC3×C7×C11C22×C41
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C41C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C41

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18942

Conjugacy classes & character table

9594 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37884, 103);