Finite Group Databasebeta

C2×#31770654 #46819492

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

Aliases

direct productC2×#31770654

Splittings

SylowC269 ⋊ C2×#430

Subgroups

subgroupG/H
centerC2×C4C2×D1076
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
FittingC22×M16×C269C2
socleC22×C269C2×C4⋊C4
prime radicalC24×C269Q8
cosocleC2×C4×C269C24
hypercenterC22×M16D269
hypocenterC269C2×#430
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

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, 13117);