Finite Group Databasebeta

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C2×C3×C7×C31⋊C3 #16840908

order3906
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C7×C31⋊C3
unambiguous semidirect product(C2×C31)⋊(C32×C7)
unambiguous semidirect product(C2×C3×C31)⋊(C3×C7)

Splittings

Fitting, socleC2×C3×C7×C31 ⋊ C3
derived, SylowC31 ⋊ C2×C32×C7
HallC2×C7×C31 ⋊ C32
HallC7×C31 ⋊ C2×C32
HallC2×C31 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C31⋊C3
commutator, cosocle, hypocenterC31C2×C32×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C31C3
LCSG ▷ C31
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1302

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×C7×(C31⋊C3)⋊C5, C3×C7×D5×C31⋊C3, C2×C3×C5×C7×C31⋊C3, …
maximal normal subgroup ofC2×C3×C7×(C31⋊C3)⋊C5, C2×C3×C5×C7×C31⋊C3, C2×C3×C49×C31⋊C3, …
maximal quotient ofC3×C7×D5×C31⋊C3, C2×C3×C5×C7×C31⋊C3, C2×C3×C49×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3906, 58);