Finite Group Databasebeta

C2×#20300934 #28411908

order14656
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20300934

Splittings

SylowC229 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#16814651
commutator, cosocleC8×C229C23
FrattiniC8C22×D229
FittingC2×Q16×C229C2
socle, prime radicalC22×C229D8
hypercenterC2×Q16D229
hypocenterC229C2×Q32
LCSG ▷ C8×C229 ▷ C4×C229 ▷ C2×C229 ▷ C229
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14656

Conjugacy classes & character table

1618 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14656, 976);