Finite Group Databasebeta

C2×D137⋊#104 #31797413

order17536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D137⋊#104
unambiguous semidirect productD137⋊(C2×#104)

Splittings

FittingC2×#41×C137 ⋊ C4
SylowC137 ⋊ C22×#104

Subgroups

subgroupG/H
centerC2×C4C22⋊#10587739
commutatorC4×C137C23×C4
FrattiniC4C23×#10587739
FittingC2×#41×C137C4
socleC22×C137C2×C22⋊C4
prime radicalC2×#41×D137C2
cosocleC4×D137C24
hypercenterC2×#41#10587739
hypocenterC137C22×#104
LCSG ▷ C4×C137 ▷ C2×C137 ▷ C137
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2192

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 21134);