Finite Group Databasebeta

C4⋊C8×D47 #15689142

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

Aliases

direct productC4⋊C8×D47

Splittings

FittingC4⋊C8×C47 ⋊ C2
SylowC47 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D47
commutatorC2×C47C22×C8
FittingC4⋊C8×C47C2
socleC22×C47C22×C4
prime radicalC22×D47C2×C4
cosocleC2×C4×C47C23
hypercenterC4⋊C8D47
hypocenterC47C2×C4⋊C8
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1504

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 568);