Finite Group Databasebeta

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C2×C7×D193⋊C3 #30633875

order16212
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D193⋊C3
unambiguous semidirect productD193⋊(C2×C3×C7)
unambiguous semidirect product(C193⋊C3)⋊(C22×C7)
unambiguous semidirect product(C2×D193)⋊(C3×C7)
unambiguous semidirect product(C2×C193⋊C3)⋊(C2×C7)

Splittings

Fitting, socleC2×C7×C193 ⋊ C2×C3
derived, SylowC193 ⋊ C22×C3×C7
HallC2×C7×D193 ⋊ C3
HallC7×C193⋊C3 ⋊ C22
HallC7×C193 ⋊ C22×C3
HallC2×D193 ⋊ C3×C7
HallC193⋊C3 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7D193⋊C3
commutator, cosocle, hypocenterC193C22×C3×C7
FrattiniC1G
Fitting, socleC2×C7×C193C2×C3
LCSG ▷ C193
UCSC1 ◁ C2×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2702

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16212, 38);