Finite Group Databasebeta

C2×C22⋊C8×D269 #46819315

order34432
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×C22⋊C8×D269

Splittings

FittingC2×C22⋊C8×C269 ⋊ C2
SylowC269 ⋊ C22×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D269
commutatorC2×C269C23×C8
FrattiniC2×C4C23×D269
FittingC2×C22⋊C8×C269C2
socleC23×C269C22×C4
prime radicalC24×D269C4
cosocleC2×C4×C269C24
hypercenterC2×C22⋊C8D269
hypocenterC269C22×C22⋊C8
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

Conjugacy classes & character table

5440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 12940);