Finite Group Databasebeta

C2×D73⋊#410 #34031129

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

Aliases

direct productC2×D73⋊#410
unambiguous semidirect productD73⋊(C2×#410)

Splittings

FittingC22×#41×C73 ⋊ C4
SylowC73 ⋊ C22×#410

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊#64408
commutatorC22×C73C24×C4
FrattiniC22C24×#64408
FittingC22×#41×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC22×#41×D73C2
cosocleC22×D73C25
hypercenterC22×#41#64408
hypocenterC73C22×#410
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

5278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1114713);