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C2×C7×D397⋊C3 #45688596

order33348
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D397⋊C3
unambiguous semidirect productD397⋊(C2×C3×C7)
unambiguous semidirect product(C397⋊C3)⋊(C22×C7)
unambiguous semidirect product(C2×D397)⋊(C3×C7)
unambiguous semidirect product(C2×C397⋊C3)⋊(C2×C7)

Splittings

Fitting, socleC2×C7×C397 ⋊ C2×C3
derived, SylowC397 ⋊ C22×C3×C7
HallC2×C7×D397 ⋊ C3
HallC7×C397⋊C3 ⋊ C22
HallC7×C397 ⋊ C22×C3
HallC2×D397 ⋊ C3×C7
HallC397⋊C3 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7D397⋊C3
commutator, cosocle, hypocenterC397C22×C3×C7
FrattiniC1G
Fitting, socleC2×C7×C397C2×C3
LCSG ▷ C397
UCSC1 ◁ C2×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5558

Conjugacy classes & character table

1008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33348, 38);