Finite Group Databasebeta

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C3×C49×#6157 #44528328

order31164
automorphism?
homologyAbelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1

Aliases

direct productC3×C49×#6157

Splittings

Fitting, HallC3×C49×C53 ⋊ C4
derived, SylowC53 ⋊ C3×C4×C49
HallC49×C53 ⋊ C3×C4
HallC3×C53 ⋊ C4×C49

Subgroups

subgroupG/H
center, hypercenterC3×C49#6157
commutator, hypocenterC53C3×C4×C49
FrattiniC7C3×C7×#6157
FittingC3×C49×C53C4
socleC3×C7×C53C4×C7
prime radicalC3×C7×D53C2×C7
cosocleC7×D53C2×C3×C7
LCSG ▷ C53
UCSC1 ◁ C3×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7791

Conjugacy classes & character table

2499 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31164, 20);