Finite Group Databasebeta

← Prev (#11919836) Next (#11919838) →

C2×#10589566 #11919837

order1152
isoclinismisoclinic class of #5464
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C22×C42

Aliases

direct productC2×#10589566

Splittings

derivedH(3,𝔽4) ⋊ C2×C9
SylowC2×H(3,𝔽4) ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC2×C3#5464
commutator, hypocenterH(3,𝔽4)C2×C9
FrattiniC22×C3C2×C22⋊A4
Fitting, prime radicalC2×C3×H(3,𝔽4)C3
socleC23×C3C22⋊A4
cosocleC3×H(3,𝔽4)C2×C3
LCSG ▷ H(3,𝔽4)
UCSC1 ◁ C2×C3

544 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 34 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) = 72

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153848);