Finite Group Databasebeta

C2×#31770620 #46819425

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#31770620

Splittings

FittingC2×#104×C269 ⋊ C2
SylowC269 ⋊ C2×#421

Subgroups

subgroupG/H
centerC2×C4D4×D269
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
FittingC2×#104×C269C2
socleC22×C269C2×C22⋊C4
prime radicalC2×#41×D269C2
cosocleC2×C4×C269C24
hypercenterC2×#104D269
hypocenterC269C2×#421
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

Conjugacy classes & character table

3796 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 13050);