Finite Group Databasebeta

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C2×C11⋊C5×D31 #20291908

order6820
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊C5×D31

Splittings

Fitting, socleC2×C11×C31 ⋊ C2×C5
derived, HallC11×C31 ⋊ C22×C5
HallC31×C11⋊C5 ⋊ C22
HallC2×C11×D31 ⋊ C5
SylowC31 ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×C5×D31

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×D31
commutator, hypocenterC11×C31C22×C5
FrattiniC1G
Fitting, socleC2×C11×C31C2×C5
LCSG ▷ C11×C31
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11⋊C5×D31⋊C3, D3×C11⋊C5×D31, C2×C3×C11⋊C5×D31, …
maximal normal subgroup ofC2×C11⋊C5×D31⋊C3, C2×C3×C11⋊C5×D31, C2×C11⋊C5×D31⋊C5, …
maximal quotient ofD3×C11⋊C5×D31, C2×C3×C11⋊C5×D31, C2×C11⋊C5×D93, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6820, 55);