Finite Group Databasebeta

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C3×C7×C3⋊(C11⋊Dic11) #44479043

order30492
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C11

Aliases

direct productC3×C7×C3⋊(C11⋊Dic11)
unambiguous semidirect productC3⋊(C3×C7×C11⋊Dic11)
unambiguous semidirect productC11⋊(C3×C7×Dic33)

Splittings

derivedC3×C112 ⋊ C3×C4×C7
HallC32×C7×C112 ⋊ C4
HallC32×C112 ⋊ C4×C7
HallC7×C112 ⋊ C3×Dic3
SylowC112 ⋊ C3×C7×Dic3
HallC32×C7 ⋊ C11⋊Dic11
SylowC32 ⋊ C7×C11⋊Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C3⋊(C11⋊D11)
commutator, hypocenterC3×C112C3×C4×C7
FrattiniC2C3×C7×C3⋊(C11⋊D11)
Fitting, socle, prime radicalC2×C32×C7×C112C2
cosocleC2×C3×C112C2×C3×C7
LCSG ▷ C3×C112
UCSC1 ◁ C2×C3×C7

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10164

Conjugacy classes & character table

7686 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 266);