Finite Group Databasebeta

C2×#34039196 #49182664

order37952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#34039196

Splittings

SylowC593 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D593
commutatorC2×C593C2×C42
FrattiniC2×C4C22×D593
FittingC2×C42×C593C2
socle, prime radicalC23×C593C2×C4
cosocleC2×C4×C593C23
hypercenterC2×C42D593
hypocenterC593C2×#97
LCSG ▷ C2×C593 ▷ C593
UCSC1 ◁ C22×C4 ◁ C2×C42

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37952

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, 498);