Finite Group Databasebeta

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C2×C49×D187 #49143902

order36652
automorphism?
homologyAbelianization (H1) = C22×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C49×D187
unambiguous semidirect product(C2×C11)⋊(D17×C49)
unambiguous semidirect product(C2×C17)⋊(D11×C49)

Splittings

FittingC2×C11×C17×C49 ⋊ C2
derived, HallC11×C17 ⋊ C22×C49
HallC11×C17×C49 ⋊ C22
HallC17×C49 ⋊ C2×D11
HallC11×C49 ⋊ C2×D17
SylowC17 ⋊ C2×D11×C49
SylowC11 ⋊ C2×D17×C49

Subgroups

subgroupG/H
center, hypercenterC2×C49D187
commutator, hypocenterC11×C17C22×C49
FrattiniC7C2×C7×D187
FittingC2×C11×C17×C49C2
socleC2×C7×C11×C17C2×C7
prime radicalC2×C7×D187C7
cosocleC7×C11×C17C22×C7
LCSG ▷ C11×C17
UCSC1 ◁ C2×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18326

Conjugacy classes & character table

9310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36652, 25);