Finite Group Databasebeta

C2×#14556072 #17986423

order4544
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#14556072

Splittings

SylowC71 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#11765850
commutator, cosocleC8×C71C23
FrattiniC8C22×D71
Fitting, prime radicalC2×D8×C71C2
socleC22×C71D8
hypercenterC2×D8D71
hypocenterC71C2×SD32
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2272

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4544, 973);