Finite Group Databasebeta

C2×C22⋊(C47⋊C8) #15689084

order3008
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊(C47⋊C8)

Splittings

SylowC47 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D47
commutatorC2×C47C22×C8
FrattiniC2×C4C22×D47
FittingC23×C4×C47C2
socleC23×C47C2×C4
prime radicalC24×C47C4
cosocleC2×C4×C47C23
hypercenterC23×C4D47
hypocenterC47C2×C22⋊C8
LCSG ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C23×C4

202 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, 510);