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C3×(C11⋊C5)⋊Dic37 #37567501

order24420
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C11⋊C5)⋊Dic37
unambiguous semidirect product(C11⋊C5)⋊(C3×Dic37)
unambiguous semidirect product(C3×Dic407)⋊C5

Splittings

derived, HallC11×C37 ⋊ C3×C4×C5
HallC3×C37×C11⋊C5 ⋊ C4
HallC3×Dic407 ⋊ C5
HallC37×C11⋊C5 ⋊ C3×C4
HallDic407 ⋊ C3×C5
HallC3×C11×C37 ⋊ C4×C5
HallC3×C11⋊C5 ⋊ Dic37
HallC3×C37 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3×Dic37
SylowC37 ⋊ C3×Dic11⋊C5
HallC3×C11 ⋊ C5×Dic37
SylowC11 ⋊ C3×C5×Dic37

Subgroups

subgroupG/H
center, hypercenterC2×C3C37⋊AGL(1,𝔽11)
commutator, hypocenterC11×C37C3×C4×C5
FrattiniC2C3×C37⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C37C2×C5
prime radicalC2×C3×C37×C11⋊C5C2
cosocleC2×C11×C37C2×C3×C5
LCSG ▷ C11×C37
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4884

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 22);