Finite Group Databasebeta

C4×#22575483 #46819702

order34432
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#22575483

Splittings

SylowC269 ⋊ C4×#137

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D269
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
FittingC4×#41×C269C2
socleC22×C269C22×D4
prime radicalC2×#41×C269C22
cosocleC2×C4×C269C24
hypercenterC4×#41D269
hypocenterC269C4×#137
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17216

Conjugacy classes & character table

5404 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 13327);