Finite Group Databasebeta

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C53×(C49⋊C3)⋊C4 #44528319

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

Aliases

direct productC53×(C49⋊C3)⋊C4
unambiguous semidirect product(C49⋊C3)⋊(C4×C53)
unambiguous semidirect productDic49⋊(C3×C53)
unambiguous semidirect product(C53×Dic49)⋊C3

Splittings

derived, SylowC49 ⋊ C3×C4×C53
HallC53×Dic49 ⋊ C3
HallC53×C49⋊C3 ⋊ C4
HallC49×C53 ⋊ C3×C4
HallDic49 ⋊ C3×C53
HallC49⋊C3 ⋊ C4×C53

Subgroups

subgroupG/H
center, hypercenterC2×C53D49⋊C3
commutator, hypocenterC49C3×C4×C53
FrattiniC2×C7AGL(1,𝔽7)×C53
FittingC2×C49×C53C2×C3
socleC2×C7×C53AGL(1,𝔽7)
prime radicalC2×C53×C49⋊C3C2
cosocleC2×C49C2×C3×C53
LCSG ▷ C49
UCSC1 ◁ C2×C53

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10388

Conjugacy classes & character table

1484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31164, 11);