Finite Group Databasebeta

C2×#13093964 #15689538

order3008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13093964

Splittings

SylowC47 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D47
commutatorC2×C47C22×C8
FrattiniC8C22×D47
FittingC22×C8×C47C2
socleC22×C47C2×C8
prime radicalC23×C47C8
cosocleC8×C47C23
hypercenterC22×C8D47
hypocenterC47C2×M32
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1504

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 964);