Finite Group Databasebeta

C2×#34062706 #50306411

order38336
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#34062706

Splittings

SylowC599 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D599
commutator, cosocleC22×C599C24
FrattiniC22C23×D599
FittingC2×C4⋊C4×C599C2
socle, prime radicalC23×C599C23
hypercenterC2×C4⋊C4D599
hypocenterC599C2×#125
LCSG ▷ C22×C599 ▷ C599
UCSC1 ◁ C23 ◁ C2×C4⋊C4

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 38336

Conjugacy classes & character table

6008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38336, 1070);