Finite Group Databasebeta

C2×D73⋊#443 #34031442

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×D73⋊#443
unambiguous semidirect productD73⋊(C2×#443)

Splittings

FittingC2×#135×C73 ⋊ C4
SylowC73 ⋊ C22×#443

Subgroups

subgroupG/H
centerC2×C4D4×#64408
commutatorC4×C73C24×C4
FrattiniC4C24×#64408
FittingC2×#135×C73C4
socleC22×C73C2×C4×D4
prime radicalC2×#135×D73C2
cosocleC4×D73C25
hypercenterC2×#135#64408
hypocenterC73C22×#443
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

2750 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1115026);