Finite Group Databasebeta

C2×#31770435 #46812677

order34432
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#31770435

Splittings

SylowC269 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D2152
commutatorC8×C269C22×C4
FrattiniC2×C8C22×D269
FittingC22×C16×C269C2
socleC22×C269#107
prime radicalC23×C269Q16
cosocleC2×C8×C269C23
hypercenterC22×C16D269
hypocenterC269C2×#368
LCSG ▷ C8×C269 ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

8620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 6302);