Finite Group Databasebeta

C2×C4⋊(C47⋊C8) #15689144

order3008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊(C47⋊C8)

Splittings

SylowC47 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D47
commutatorC2×C47C22×C8
FrattiniC2×C4C22×D47
FittingC2×C42×C47C2
socle, prime radicalC23×C47C2×C4
cosocleC2×C4×C47C23
hypercenterC2×C42D47
hypocenterC47C2×C4⋊C8
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3008

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, 570);