Finite Group Databasebeta

C2×C22⋊#6855 #14516620

order1944
automorphism?
homologyAbelianization (H1) = C2×C92 · Schur multiplier (H2) = C2×C33

Aliases

direct productC2×C22⋊#6855
unambiguous semidirect productC23⋊#6855

Splittings

SylowC23 ⋊ #6855

Subgroups

subgroupG/H
centerC2×C33C3×A4
commutatorC22×C3C2×C92
FrattiniC33C2×C3×A4
FittingC23×C32×C9C3
socle, prime radicalC23×C33C32
cosocleC22×C33C2×C32
hypercenterC2×C32×C9A4
hypocenterC22C2×#6855
LCSG ▷ C22×C3 ▷ C22
UCSC1 ◁ C2×C33 ◁ C2×C32×C9

476 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 486

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1014);