Finite Group Databasebeta

C2×C4×#17989786 #49167194

order37504
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#17989786

Splittings

SylowC293 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C42C2×D293
commutatorC2×C293C22×C42
FrattiniC2×C4C23×D293
FittingC22×C42×C293C2
socleC23×C293C22×C4
prime radicalC24×C293C2×C4
cosocleC2×C4×C293C24
hypercenterC22×C42D293
hypocenterC293C2×C4×M16
LCSG ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C42 ◁ C22×C42

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

9424 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 12919);