Finite Group Databasebeta

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C2×C5×C11×C31⋊C3 #23779409

order10230
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C11×C31⋊C3
unambiguous semidirect product(C2×C5×C31)⋊(C3×C11)
unambiguous semidirect product(C2×C5×C11×C31)⋊C3

Splittings

Fitting, socle, HallC2×C5×C11×C31 ⋊ C3
derived, SylowC31 ⋊ C2×C3×C5×C11
HallC5×C11×C31 ⋊ C2×C3
HallC2×C11×C31 ⋊ C3×C5
HallC11×C31 ⋊ C2×C3×C5
HallC2×C5×C31 ⋊ C3×C11
HallC5×C31 ⋊ C2×C3×C11
HallC2×C31 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11C31⋊C3
commutator, cosocle, hypocenterC31C2×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C31C3
LCSG ▷ C31
UCSC1 ◁ C2×C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1430 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C11×C31⋊C3, C5×C11×(C31⋊C3)⋊C4, C5×Dic11×C31⋊C3, …
maximal normal subgroup ofC4×C5×C11×C31⋊C3, C5×C11×(C31⋊C3)⋊C4, C5×Dic11×C31⋊C3, …
maximal quotient ofC4×C5×C11×C31⋊C3, C22×C5×C11×C31⋊C3, C2×C5×C11×C31⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 8);