Finite Group Databasebeta

C2×#34039225 #49183130

order37952
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#34039225

Splittings

SylowC593 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D593
commutatorC2×C593C22×C8
FrattiniC8C22×D593
FittingC22×C8×C593C2
socleC22×C593C2×C8
prime radicalC23×C593C8
cosocleC8×C593C23
hypercenterC22×C8D593
hypocenterC593C2×M32
LCSG ▷ C2×C593 ▷ C593
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18976

Conjugacy classes & character table

9512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37952, 964);