Finite Group Databasebeta

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C3×C22⋊#14523272 #37567989

order24444
automorphism?
homologyAbelianization (H1) = C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C22⋊#14523272
unambiguous semidirect product(C22×C3)⋊#14523272

Splittings

Fitting, socleC22×C3×C7×C97 ⋊ C3
derived, HallC22×C7×C97 ⋊ C32
HallC7×C97 ⋊ C3×A4
HallC22×C97 ⋊ C3×ΓL(1,𝔽8)
SylowC97 ⋊ C3×C22⋊ΓL(1,𝔽8)
HallC22×C7 ⋊ C3×C97⋊C3
SylowC7 ⋊ C3×C22⋊(C97⋊C3)
SylowC22 ⋊ C3×#14523272

Subgroups

subgroupG/H
center, hypercenterC3C22⋊#14523272
commutator, cosocle, hypocenterC22×C7×C97C32
FrattiniC1G
Fitting, socleC22×C3×C7×C97C3
LCSG ▷ C22×C7×C97
UCSC1 ◁ C3

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8148

Conjugacy classes & character table

2724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 252);