Finite Group Databasebeta

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C3×C53×Dic49 #44528312

order31164
automorphism?
homologyAbelianization (H1) = C3×C4×C53 · Schur multiplier (H2) = C1

Aliases

direct productC3×C53×Dic49

Splittings

derived, SylowC49 ⋊ C3×C4×C53
HallC3×C49×C53 ⋊ C4
HallC49×C53 ⋊ C3×C4
HallC3×C49 ⋊ C4×C53

Subgroups

subgroupG/H
center, hypercenterC2×C3×C53D49
commutator, hypocenterC49C3×C4×C53
FrattiniC2×C7C3×D7×C53
FittingC2×C3×C49×C53C2
socle, prime radicalC2×C3×C7×C53D7
cosocleC2×C49C2×C3×C53
LCSG ▷ C49
UCSC1 ◁ C2×C3×C53

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31164

Conjugacy classes & character table

8268 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31164, 4);