Finite Group Databasebeta

C2×#31770442 #46813185

order34432
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#31770442

Splittings

FittingC2×Q32×C269 ⋊ C2
SylowC269 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#22575394
commutator, cosocleC16×C269C23
FrattiniC16C22×D269
FittingC2×Q32×C269C2
socleC22×C269D16
prime radicalC2×D4304C2
hypercenterC2×Q32D269
hypocenterC269C2×SD64
LCSG ▷ C16×C269 ▷ C8×C269 ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q32

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

2986 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 6810);