Finite Group Databasebeta

C2×#34039241 #49183168

order37952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#34039241

Splittings

SylowC593 ⋊ C2×#117

Subgroups

subgroupG/H
centerC23C22×D593
commutatorC2×C593C23×C4
FrattiniC22C23×D593
FittingC2×C22⋊C4×C593C2
socleC23×C593C23
prime radicalC24×C593C22
cosocleC22×C593C24
hypercenterC2×C22⋊C4D593
hypocenterC593C2×#117
LCSG ▷ C2×C593 ▷ C593
UCSC1 ◁ C23 ◁ C2×C22⋊C4

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18976

Conjugacy classes & character table

5960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37952, 1002);