Finite Group Databasebeta

C2×D73⋊#360 #34030036

order18688
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D73⋊#360
unambiguous semidirect productD73⋊(C2×#360)

Splittings

FittingC2×#135×C73 ⋊ C4
SylowC73 ⋊ C22×#360

Subgroups

subgroupG/H
centerC22C2×#14556653
commutatorC8×C73C23×C4
FrattiniC8C23×#64408
FittingC2×#135×C73C4
socleC22×C73C2×#102
prime radicalC2×#135×D73C2
cosocleC8×D73C24
hypercenterC2×#135#64408
hypocenterC73C22×#360
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#135

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1113620);