Finite Group Databasebeta

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C3×#13094089⋊C7 #44539780

order31668
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×#13094089⋊C7
unambiguous semidirect product(C3×#13094089)⋊C7

Splittings

Fitting, socle, HallC3×C13×C29 ⋊ C4×C7
derived, HallC13×C29 ⋊ C3×C4×C7
HallC3×C13×C29⋊C7 ⋊ C4
HallC3×#13094089 ⋊ C7
HallC13×C29⋊C7 ⋊ C3×C4
Hall#13094089 ⋊ C3×C7
HallC3×C29⋊C7 ⋊ #261
HallC29⋊C7 ⋊ C3×#261
HallC3×C29 ⋊ C7×#261
HallC3×C13 ⋊ Dic29⋊C7
SylowC29 ⋊ C3×C7×#261
SylowC13 ⋊ C3×Dic29⋊C7

Subgroups

subgroupG/H
center, hypercenterC3#13094089⋊C7
commutator, hypocenterC13×C29C3×C4×C7
FrattiniC1G
Fitting, socleC3×C13×C29C4×C7
prime radicalC3×D13×C29⋊C7C2
cosocleD13×C29C2×C3×C7
LCSG ▷ C13×C29
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1131

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 75);