Finite Group Databasebeta

C2×#34036093 #49167221

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

Aliases

direct productC2×#34036093

Splittings

SylowC293 ⋊ C2×#407

Subgroups

subgroupG/H
centerC22×C4C22×D293
commutatorC22×C293C23×C4
FrattiniC2×C4C23×D293
FittingC24×C4×C293C2
socleC23×C293C22×C4
prime radicalC25×C293C4
cosocleC2×C4×C293C24
hypercenterC24×C4D293
hypocenterC293C2×#407
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22×C4 ◁ C24×C4

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9376

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, 12946);