Finite Group Databasebeta

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C3×C29×Dic91 #44539718

order31668
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×C29×Dic91

Splittings

derived, HallC7×C13 ⋊ C3×C4×C29
HallC3×C7×C13×C29 ⋊ C4
HallC7×C13×C29 ⋊ C3×C4
HallC3×C13×C29 ⋊ Dic7
HallC3×C7×C29 ⋊ Dic13
HallC13×C29 ⋊ C3×Dic7
HallC3×C7×C13 ⋊ C4×C29
HallC7×C29 ⋊ C3×Dic13
HallC3×C13 ⋊ Dic7×C29
HallC3×C7 ⋊ C29×Dic13
SylowC13 ⋊ C3×Dic7×C29
SylowC7 ⋊ C3×C29×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C29D91
commutator, hypocenterC7×C13C3×C4×C29
FrattiniC2C3×C29×D91
Fitting, socle, prime radicalC2×C3×C7×C13×C29C2
cosocleC2×C7×C13C2×C3×C29
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31668

Conjugacy classes & character table

8178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 13);