Finite Group Databasebeta

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C2×C17×C11⋊D11 #22551743

order8228
isoclinismisoclinic class of C11⋊D11
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C17×C11⋊D11
unambiguous semidirect product(C2×C11)⋊(C17×D11)

Splittings

Fitting, socleC2×C112×C17 ⋊ C2
derived, SylowC112 ⋊ C22×C17
HallC112×C17 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C17C11⋊D11
commutator, hypocenterC112C22×C17
FrattiniC1G
Fitting, socleC2×C112×C17C2
LCSG ▷ C112
UCSC1 ◁ C2×C17

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2108 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C17×(C11⋊D11)⋊C3, D3×C17×C11⋊D11, C2×C3×C17×C11⋊D11, …
maximal normal subgroup ofC2×C17×(C11⋊D11)⋊C3, C2×C3×C17×C11⋊D11
maximal quotient ofD3×C17×C11⋊D11, C2×C3×C17×C11⋊D11, C2×C17×C3⋊(C11⋊D11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8228, 31);