Finite Group Databasebeta

C2×D181⋊#104 #37550345

order23168
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D181⋊#104
unambiguous semidirect productD181⋊(C2×#104)

Splittings

FittingC2×#41×C181 ⋊ C4
SylowC181 ⋊ C22×#104

Subgroups

subgroupG/H
centerC2×C4C22⋊#10624382
commutatorC4×C181C23×C4
FrattiniC4C23×#10624382
FittingC2×#41×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC2×#41×D181C2
cosocleC4×D181C24
hypercenterC2×#41#10624382
hypocenterC181C22×#104
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 21134);