Finite Group Databasebeta

C2×Dic4304 #46813190

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

Aliases

direct productC2×Dic4304

Splittings

SylowC269 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22D4304
commutator, cosocleC16×C269C23
FrattiniC16C22×D269
FittingC2×C32×C269C2
socle, prime radicalC22×C269D16
hypercenterC2×C32D269
hypocenterC269C2×Q64
LCSG ▷ C16×C269 ▷ C8×C269 ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34432

Conjugacy classes & character table

8614 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 6815);