Finite Group Databasebeta

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C32×C11×C7⋊#261 #49114892

order36036
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11×C7⋊#261

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C4
derived, HallC7×C13 ⋊ C32×C4×C11
HallC32×C11×C13 ⋊ Dic7
HallC7×C11×C13 ⋊ C32×C4
HallC32×C7×C13 ⋊ C4×C11
HallC32×C7×C11 ⋊ #261
HallC11×C13 ⋊ C32×Dic7
HallC32×C13 ⋊ C11×Dic7
HallC7×C11 ⋊ C32×#261
HallC32×C7 ⋊ C11×#261
SylowC13 ⋊ C32×C11×Dic7
SylowC7 ⋊ C32×C11×#261

Subgroups

subgroupG/H
center, hypercenterC32×C11C7⋊#261
commutator, hypocenterC7×C13C32×C4×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC32×C7×C11×D13C2
cosocleC7×D13C2×C32×C11
LCSG ▷ C7×C13
UCSC1 ◁ C32×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9009

Conjugacy classes & character table

3069 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 560);