Finite Group Databasebeta

← Prev (#37551641) Next (#37551643) →

C2×C7×D277⋊C3 #37551642

order23268
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D277⋊C3
unambiguous semidirect productD277⋊(C2×C3×C7)
unambiguous semidirect product(C277⋊C3)⋊(C22×C7)
unambiguous semidirect product(C2×D277)⋊(C3×C7)
unambiguous semidirect product(C2×C277⋊C3)⋊(C2×C7)

Splittings

Fitting, socleC2×C7×C277 ⋊ C2×C3
derived, SylowC277 ⋊ C22×C3×C7
HallC2×C7×D277 ⋊ C3
HallC7×C277⋊C3 ⋊ C22
HallC7×C277 ⋊ C22×C3
HallC2×D277 ⋊ C3×C7
HallC277⋊C3 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7D277⋊C3
commutator, cosocle, hypocenterC277C22×C3×C7
FrattiniC1G
Fitting, socleC2×C7×C277C2×C3
LCSG ▷ C277
UCSC1 ◁ C2×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3878

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23268, 38);