Finite Group Databasebeta

C2×#34035997 #49161175

order37504
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#34035997

Splittings

SylowC293 ⋊ C2×#383

Subgroups

subgroupG/H
centerC24C22×D293
commutatorC22×C293C23×C4
FrattiniC23C23×D293
FittingC22×C42×C293C2
socle, prime radicalC24×C293C23
cosocleC23×C293C24
hypercenterC22×C42D293
hypocenterC293C2×#383
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C24 ◁ C22×C42

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37504

Conjugacy classes & character table

9400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 6900);