Finite Group Databasebeta

C2×#31770647 #46819470

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

Aliases

direct productC2×#31770647

Splittings

SylowC269 ⋊ C2×#428

Subgroups

subgroupG/H
centerC23C2×D1076
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
FittingC22×M16×C269C2
socleC23×C269C2×D4
prime radicalC24×C269D4
cosocleC2×C4×C269C24
hypercenterC22×M16D269
hypocenterC269C2×#428
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

536 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, 13095);