Finite Group Databasebeta

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C3×C4×#87704 #18012196

order4788
isoclinismisoclinic class of #87704
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×#87704

Splittings

FittingC3×C4×C7×C19 ⋊ C3
derived, HallC7×C19 ⋊ C32×C4
HallC4×C7×C19 ⋊ C32
HallC4×C19 ⋊ C3×ΓL(1,𝔽8)
HallC4×C7 ⋊ C3×C19⋊C3
SylowC19 ⋊ C3×C4×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C4×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C4#87704
commutator, hypocenterC7×C19C32×C4
FrattiniC2C2×C3×#87704
FittingC3×C4×C7×C19C3
socleC2×C3×C7×C19C2×C3
prime radicalC2×C3×#87704C2
cosocleC2×C7×C19C2×C32
LCSG ▷ C7×C19
UCSC1 ◁ C3×C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1596

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×Dic5×#87704, C3×C4×C5×#87704, C3×AGL(1,𝔽5)×#87704, …
maximal normal subgroup ofC3×C4×C5×#87704, C3×C4×C7×#87704
maximal quotient ofC3×Dic5×#87704, C3×C4×C5×#87704, C3×AGL(1,𝔽5)×#87704, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 112);