Finite Group Databasebeta

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C7×C11×C3⋊Dic33 #44479038

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

Aliases

direct productC7×C11×C3⋊Dic33
unambiguous semidirect productC3⋊(C7×C11×Dic33)
unambiguous semidirect productC11⋊(C7×C11×C3⋊Dic3)

Splittings

derivedC32×C11 ⋊ C4×C7×C11
HallC32×C7×C112 ⋊ C4
HallC32×C112 ⋊ C4×C7
HallC7×C112 ⋊ C3⋊Dic3
SylowC112 ⋊ C7×C3⋊Dic3
HallC32×C7 ⋊ C11×Dic11
SylowC32 ⋊ C7×C11×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11C3⋊D33
commutator, hypocenterC32×C11C4×C7×C11
FrattiniC2C7×C11×C3⋊D33
Fitting, socle, prime radicalC2×C32×C7×C112C2
cosocleC2×C32×C11C2×C7×C11
LCSG ▷ C32×C11
UCSC1 ◁ C2×C7×C11

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

7854 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 261);