Finite Group Databasebeta

C22×#10625335 #15689896

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

Aliases

direct productC22×#10625335

Splittings

SylowC47 ⋊ C22×SD16

Subgroups

subgroupG/H
centerC23C22⋊D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
Fitting, prime radicalC22×D4×C47C2
socleC23×C47D4
hypercenterC22×D4D47
hypocenterC47C22×SD16
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1504

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, 1322);