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C2×C3×D449⋊C7 #49179652

order37716
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D449⋊C7
unambiguous semidirect productD449⋊(C2×C3×C7)
unambiguous semidirect product(C2×D449)⋊(C3×C7)
unambiguous semidirect product(C449⋊C7)⋊(C22×C3)
unambiguous semidirect product(C2×C3×D449)⋊C7
unambiguous semidirect product(C2×C449⋊C7)⋊(C2×C3)

Splittings

Fitting, socleC2×C3×C449 ⋊ C2×C7
derived, SylowC449 ⋊ C22×C3×C7
HallC3×C449⋊C7 ⋊ C22
HallC2×C3×D449 ⋊ C7
HallC449⋊C7 ⋊ C22×C3
HallC2×D449 ⋊ C3×C7
HallC3×C449 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3D449⋊C7
commutator, cosocle, hypocenterC449C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C449C2×C7
LCSG ▷ C449
UCSC1 ◁ C2×C3

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2694

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37716, 22);