Finite Group Databasebeta

C2×#11757584 #14517468

order1944
automorphism?
homologyAbelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×#11757584

Splittings

Sylow#6908 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22×C9(C3⋊D3)⋊C3
commutator, hypocenterH(3,𝔽3)C2×C32×C4
FrattiniC2×C32C2×C32×D3
Fitting, prime radicalC22×#6908C2
socleC22×C3C3×(C3⋊D3)⋊C3
cosocleC2×H(3,𝔽3)C22×C32
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C22×C9

327 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 327 conjugacy classes of subgroups — too many to draw. Only its 93 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) = 216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1862);