Finite Group Databasebeta

← Prev (#49114336) Next (#49114338) →

C4×C11×#11717942 #49114337

order36036
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11×#11717942

Splittings

derived, HallC7×C13 ⋊ C4×C9×C11
HallC4×C7×C11×C13 ⋊ C9
HallC7×C11×C13 ⋊ C4×C9
HallC4×C11×C13 ⋊ C7⋊C9
HallC4×C7×C13 ⋊ C9×C11
HallC4×C7×C11 ⋊ C13⋊C9
HallC11×C13 ⋊ C4×C7⋊C9
HallC7×C11 ⋊ C4×C13⋊C9
HallC4×C13 ⋊ C11×C7⋊C9
HallC4×C7 ⋊ C11×C13⋊C9
SylowC13 ⋊ C4×C11×C7⋊C9
SylowC7 ⋊ C4×C11×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C11#63271
commutator, hypocenterC7×C13C4×C9×C11
FrattiniC2×C3C2×C11×#63271
FittingC3×C4×C7×C11×C13C3
socle, prime radicalC2×C3×C7×C11×C13C2×C3
cosocleC2×C3×C7×C13C2×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C3×C4×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36036

Conjugacy classes & character table

4356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 5);