Finite Group Databasebeta

C2×C8×C22⋊D269 #46819556

order34432
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C8×C22⋊D269

Splittings

FittingC23×C8×C269 ⋊ C2
SylowC269 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C8C2×D269
commutatorC2×C269C23×C8
FrattiniC2×C4C23×D269
FittingC23×C8×C269C2
socleC23×C269C22×C4
prime radicalC22×C22⋊D269C4
cosocleC2×C4×C269C24
hypercenterC23×C8D269
hypocenterC269C2×C8×D4
LCSG ▷ C2×C269 ▷ C269
UCSC1 ◁ C22×C8 ◁ C23×C8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

8656 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 13181);