Finite Group Databasebeta

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C11×C13×C3⋊Dic21 #49114597

order36036
automorphism?
homologyAbelianization (H1) = C4×C11×C13 · Schur multiplier (H2) = C3

Aliases

direct productC11×C13×C3⋊Dic21
unambiguous semidirect productC3⋊(C11×C13×Dic21)
unambiguous semidirect productC7⋊(C11×C13×C3⋊Dic3)

Splittings

derived, HallC32×C7 ⋊ C4×C11×C13
HallC32×C7×C11×C13 ⋊ C4
HallC32×C11×C13 ⋊ Dic7
HallC7×C11×C13 ⋊ C3⋊Dic3
HallC32×C7×C13 ⋊ C4×C11
HallC32×C7×C11 ⋊ C4×C13
HallC32×C13 ⋊ C11×Dic7
HallC32×C11 ⋊ C13×Dic7
HallC7×C13 ⋊ C11×C3⋊Dic3
HallC7×C11 ⋊ C13×C3⋊Dic3
SylowC32 ⋊ C11×C13×Dic7
SylowC7 ⋊ C11×C13×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C11×C13C3⋊D21
commutator, hypocenterC32×C7C4×C11×C13
FrattiniC2C11×C13×C3⋊D21
Fitting, socle, prime radicalC2×C32×C7×C11×C13C2
cosocleC2×C32×C7C2×C11×C13
LCSG ▷ C32×C7
UCSC1 ◁ C2×C11×C13

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36036

Conjugacy classes & character table

9438 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 265);