Finite Group Databasebeta

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C3×C22⋊#14556233 #42117607

order27468
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C22⋊#14556233
unambiguous semidirect product(C22×C3)⋊#14556233

Splittings

Fitting, socleC22×C3×C7×C109 ⋊ C3
derived, HallC22×C7×C109 ⋊ C32
HallC7×C109 ⋊ C3×A4
HallC22×C109 ⋊ C3×ΓL(1,𝔽8)
SylowC109 ⋊ C3×C22⋊ΓL(1,𝔽8)
HallC22×C7 ⋊ C3×C109⋊C3
SylowC7 ⋊ C3×C22⋊(C109⋊C3)
SylowC22 ⋊ C3×#14556233

Subgroups

subgroupG/H
center, hypercenterC3C22⋊#14556233
commutator, cosocle, hypocenterC22×C7×C109C32
FrattiniC1G
Fitting, socleC22×C3×C7×C109C3
LCSG ▷ C22×C7×C109
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9156

Conjugacy classes & character table

3060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27468, 288);