Finite Group Databasebeta

C2×#13094024 #15689667

order3008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13094024

Splittings

SylowC47 ⋊ C2×C4⋊Q8

Subgroups

subgroupG/H
centerC23C22×D47
commutator, cosocleC22×C47C24
FrattiniC22C23×D47
FittingC2×C42×C47C2
socle, prime radicalC23×C47C23
hypercenterC2×C42D47
hypocenterC47C2×C4⋊Q8
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42

290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3008

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 1093);