Finite Group Databasebeta

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C2×C49×C109⋊C3 #44545175

order32046
automorphism?
homologyAbelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1

Aliases

direct productC2×C49×C109⋊C3
unambiguous semidirect product(C2×C109)⋊(C3×C49)

Splittings

Fitting, HallC2×C49×C109 ⋊ C3
derived, SylowC109 ⋊ C2×C3×C49
HallC49×C109 ⋊ C2×C3
HallC2×C109 ⋊ C3×C49

Subgroups

subgroupG/H
center, hypercenterC2×C49C109⋊C3
commutator, hypocenterC109C2×C3×C49
FrattiniC7C2×C7×C109⋊C3
FittingC2×C49×C109C3
socleC2×C7×C109C3×C7
prime radicalC2×C7×C109⋊C3C7
cosocleC7×C109C2×C3×C7
LCSG ▷ C109
UCSC1 ◁ C2×C49

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10682

Conjugacy classes & character table

3822 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32046, 2);