Finite Group Databasebeta

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C3×C4×C13×#3862 #37524815

order22932
automorphism?
homologyAbelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3×C7

Aliases

direct productC3×C4×C13×#3862

Splittings

FittingC3×C4×C72×C13 ⋊ C3
derived, SylowC72 ⋊ C32×C4×C13
HallC4×C72×C13 ⋊ C32
HallC72×C13 ⋊ C32×C4
HallC4×C72 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC3×C4×C13#3862
commutator, hypocenterC72C32×C4×C13
FrattiniC2C2×C3×C13×#3862
FittingC3×C4×C72×C13C3
socleC2×C3×C72×C13C2×C3
prime radicalC2×C3×C13×#3862C2
cosocleC2×C72C2×C32×C13
LCSG ▷ C72
UCSC1 ◁ C3×C4×C13

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3276

Conjugacy classes & character table

2964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 760);