Finite Group Databasebeta

C2×#34039229 #49183139

order37952
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#34039229

Splittings

SylowC593 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#23748718
commutator, cosocleC8×C593C23
FrattiniC8C22×D593
Fitting, prime radicalC2×D8×C593C2
socleC22×C593D8
hypercenterC2×D8D593
hypocenterC593C2×SD32
LCSG ▷ C8×C593 ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18976

Conjugacy classes & character table

4166 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37952, 973);