Finite Group Databasebeta

C2×#34036052 #49162006

order37504
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#34036052

Splittings

SylowC293 ⋊ C2×#396

Subgroups

subgroupG/H
centerC24C22×D293
commutator, cosocleC23×C293C24
FrattiniC23C23×D293
FittingC22×C22⋊C4×C293C2
socleC24×C293C23
prime radicalC25×C293C22
hypercenterC22×C22⋊C4D293
hypocenterC293C2×#396
LCSG ▷ C23×C293 ▷ C293
UCSC1 ◁ C24 ◁ C22×C22⋊C4

908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

5884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 7731);