Finite Group Databasebeta

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C2×C7×C11×D31 #23750899

order9548
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C22×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C11×D31
unambiguous semidirect productC31⋊(C22×C7×C11)
unambiguous semidirect product(C2×C31)⋊(C2×C7×C11)

Splittings

Fitting, socleC2×C7×C11×C31 ⋊ C2
derived, SylowC31 ⋊ C22×C7×C11
HallC7×C11×C31 ⋊ C22
HallC11×C31 ⋊ C22×C7
HallC7×C31 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11D31
commutator, cosocle, hypocenterC31C22×C7×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C31C2
LCSG ▷ C31
UCSC1 ◁ C2×C7×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2618 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C11×D31⋊C3, C2×C11×#13049954, C2×C11×#13049955, …
maximal normal subgroup ofC2×C7×C11×D31⋊C3, C2×C11×#13049954, C2×C11×#13049955, …
maximal quotient ofD3×C7×C11×D31, C2×C3×C7×C11×D31, C2×C7×C11×D93

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9548, 23);