Finite Group Databasebeta

C2×C16×#10596842 #34033472

order18688
automorphism?
homologyAbelianization (H1) = C2×C8×C16 · Schur multiplier (H2) = C22×C8

Aliases

direct productC2×C16×#10596842

Splittings

FittingC2×C16×C73 ⋊ C8
derived, SylowC73 ⋊ C2×C8×C16

Subgroups

subgroupG/H
center, hypercenterC2×C16#10596842
commutator, hypocenterC73C2×C8×C16
FrattiniC8C22×#10596842
FittingC2×C16×C73C8
socleC22×C73C82
prime radicalC22×D73C4×C8
cosocleC8×#64408C23
LCSG ▷ C73
UCSC1 ◁ C2×C16

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1117056);