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Dic3×C49×C53 #44528314

order31164
automorphism?
homologyAbelianization (H1) = C4×C49×C53 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C49×C53
unambiguous semidirect productC3⋊(C4×C49×C53)

Splittings

derived, SylowC3 ⋊ C4×C49×C53
HallC3×C49×C53 ⋊ C4
HallC3×C53 ⋊ C4×C49
HallC3×C49 ⋊ C4×C53

Subgroups

subgroupG/H
center, hypercenterC2×C49×C53D3
commutator, hypocenterC3C4×C49×C53
FrattiniC2×C7D3×C7×C53
FittingC2×C3×C49×C53C2
socle, prime radicalC2×C3×C7×C53C2×C7
cosocleC2×C3×C7C2×C7×C53
LCSG ▷ C3
UCSC1 ◁ C2×C49×C53

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31164

Conjugacy classes & character table

15582 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31164, 6);