Finite Group Databasebeta

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C3×C7×C11×Dic11 #23779000

order10164
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11×Dic11
unambiguous semidirect productC11⋊(C3×C4×C7×C11)

Splittings

derivedC11 ⋊ C3×C4×C7×C11
HallC3×C7×C112 ⋊ C4
HallC7×C112 ⋊ C3×C4
HallC3×C112 ⋊ C4×C7
SylowC112 ⋊ C3×C4×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C11D11
commutator, hypocenterC11C3×C4×C7×C11
FrattiniC2C3×C7×C11×D11
Fitting, socle, prime radicalC2×C3×C7×C112C2
cosocleC2×C11C2×C3×C7×C11
LCSG ▷ C11
UCSC1 ◁ C2×C3×C7×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3234 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×Dic11×C7⋊C9, C7×C9×C11×Dic11, C3×C7×#13089712, …
maximal normal subgroup ofC11×Dic11×C7⋊C9, C7×C9×C11×Dic11, C3×C11×ΓL(1,𝔽8)×Dic11, …
maximal quotient ofC7×C9×C11×Dic11, C3×C7×C11×Dic33, C32×C7×C11×Dic11

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10164, 52);