Finite Group Databasebeta

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C4×C29×C97⋊C3 #46798189

order33756
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC4×C29×C97⋊C3
unambiguous semidirect product(C4×C97)⋊(C3×C29)
unambiguous semidirect product(C4×C29×C97)⋊C3

Splittings

Fitting, HallC4×C29×C97 ⋊ C3
derived, SylowC97 ⋊ C3×C4×C29
HallC29×C97 ⋊ C3×C4
HallC4×C97 ⋊ C3×C29

Subgroups

subgroupG/H
center, hypercenterC4×C29C97⋊C3
commutator, hypocenterC97C3×C4×C29
FrattiniC2C2×C29×C97⋊C3
FittingC4×C29×C97C3
socleC2×C29×C97C2×C3
prime radicalC2×C29×C97⋊C3C2
cosocleC2×C97C2×C3×C29
LCSG ▷ C97
UCSC1 ◁ C4×C29

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11252

Conjugacy classes & character table

4060 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33756, 2);