Finite Group Databasebeta

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C4×C29×C67⋊C3 #37552160

order23316
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC4×C29×C67⋊C3
unambiguous semidirect product(C4×C67)⋊(C3×C29)
unambiguous semidirect product(C4×C29×C67)⋊C3

Splittings

Fitting, HallC4×C29×C67 ⋊ C3
derived, SylowC67 ⋊ C3×C4×C29
HallC29×C67 ⋊ C3×C4
HallC4×C67 ⋊ C3×C29

Subgroups

subgroupG/H
center, hypercenterC4×C29C67⋊C3
commutator, hypocenterC67C3×C4×C29
FrattiniC2C2×C29×C67⋊C3
FittingC4×C29×C67C3
socleC2×C29×C67C2×C3
prime radicalC2×C29×C67⋊C3C2
cosocleC2×C67C2×C3×C29
LCSG ▷ C67
UCSC1 ◁ C4×C29

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7772

Conjugacy classes & character table

2900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23316, 2);