Finite Group Databasebeta

C2×#31770367 #46810598

order34432
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#31770367

Splittings

SylowC269 ⋊ C2×#340

Subgroups

subgroupG/H
centerC24C22⋊D269
commutatorC4×C269C2×C42
FrattiniC22×C4C22×D269
FittingC22×C4⋊C4×C269C2
socle, prime radicalC24×C269D4
cosocleC22×C4×C269C23
hypercenterC22×C4⋊C4D269
hypocenterC269C2×#340
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34432

Conjugacy classes & character table

5416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34432, 4223);