Finite Group Databasebeta

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C3×#73020 #11920798

order1152
isoclinismisoclinic class of #5386
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#73020

Splittings

FittingC3×C8×Q8 ⋊ D3

Subgroups

subgroupG/H
centerC2×C3×C4C2×S4
commutatorC2×SL(2,𝔽3)C2×C3×C4
FrattiniC2×C4C2×C3×S4
FittingC3×C8×Q8D3
socleC22×C3C4×S4
prime radicalC2×C3×GL(2,𝔽3)C4
cosocleC4×SL(2,𝔽3)C22×C3
hypercenterC2×C3×C8S4
hypocenterSL(2,𝔽3)C3×M16
LCSG ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C8

227 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 227 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 192

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 154809);