Finite Group Databasebeta

C22×#10625337 #15689899

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

Aliases

direct productC22×#10625337

Splittings

SylowC47 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23C22⋊D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
FittingC22×Q8×C47C2
socle, prime radicalC23×C47D4
hypercenterC22×Q8D47
hypocenterC47C22×Q16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3008

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 1325);