Finite Group Databasebeta

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C4×C53×C49⋊C3 #44528310

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

Aliases

direct productC4×C53×C49⋊C3
unambiguous semidirect product(C4×C49)⋊(C3×C53)
unambiguous semidirect product(C4×C49×C53)⋊C3

Splittings

Fitting, HallC4×C49×C53 ⋊ C3
derived, SylowC49 ⋊ C3×C4×C53
HallC49×C53 ⋊ C3×C4
HallC4×C49 ⋊ C3×C53

Subgroups

subgroupG/H
center, hypercenterC4×C53C49⋊C3
commutator, hypocenterC49C3×C4×C53
FrattiniC2×C7C2×ΓL(1,𝔽8)×C53
FittingC4×C49×C53C3
socleC2×C7×C53C2×ΓL(1,𝔽8)
prime radicalC2×C53×C49⋊C3C2
cosocleC2×C49C2×C3×C53
LCSG ▷ C49
UCSC1 ◁ C4×C53

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10388

Conjugacy classes & character table

4028 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31164, 2);