Finite Group Databasebeta

C2×#13093969 #15689548

order3008
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13093969

Splittings

FittingC2×C16×C47 ⋊ C2
SylowC47 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22D376
commutator, cosocleC8×C47C23
FrattiniC8C22×D47
FittingC2×C16×C47C2
socleC22×C47D8
prime radicalC2×D376C2
hypercenterC2×C16D47
hypocenterC47C2×SD32
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1504

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 974);