Finite Group Databasebeta

C2×#34035959 #49160577

order37504
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#34035959

Splittings

SylowC293 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D2344
commutatorC8×C293C22×C4
FrattiniC2×C8C22×D293
FittingC22×C16×C293C2
socleC22×C293#107
prime radicalC23×C293Q16
cosocleC2×C8×C293C23
hypercenterC22×C16D293
hypocenterC293C2×#368
LCSG ▷ C8×C293 ▷ C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

9388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 6302);