Finite Group Databasebeta

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C2×C17×D97⋊C3 #34090044

order19788
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D97⋊C3
unambiguous semidirect productD97⋊(C2×C3×C17)
unambiguous semidirect product(C97⋊C3)⋊(C22×C17)
unambiguous semidirect product(C2×D97)⋊(C3×C17)
unambiguous semidirect product(C2×C97⋊C3)⋊(C2×C17)
unambiguous semidirect product(C2×C17×D97)⋊C3

Splittings

Fitting, socleC2×C17×C97 ⋊ C2×C3
derived, SylowC97 ⋊ C22×C3×C17
HallC2×C17×D97 ⋊ C3
HallC17×C97⋊C3 ⋊ C22
HallC17×C97 ⋊ C22×C3
HallC2×D97 ⋊ C3×C17
HallC97⋊C3 ⋊ C22×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D97⋊C3
commutator, cosocle, hypocenterC97C22×C3×C17
FrattiniC1G
Fitting, socleC2×C17×C97C2×C3
LCSG ▷ C97
UCSC1 ◁ C2×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3298

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19788, 21);