Finite Group Databasebeta

C2×#14556531 #17989002

order4672
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14556531

Splittings

SylowC73 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D73
commutatorC2×C73C22×C8
FrattiniC8C22×D73
FittingC22×C8×C73C2
socleC22×C73C2×C8
prime radicalC23×C73C8
cosocleC8×C73C23
hypercenterC22×C8D73
hypocenterC73C2×M32
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

1192 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4672, 964);