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C3×(C11⋊C5)⋊#3866 #37567523

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

Aliases

direct productC3×(C11⋊C5)⋊#3866
unambiguous semidirect product(C11⋊C5)⋊(C3×#3866)
unambiguous semidirect product(C3×C11⋊#3866)⋊C5

Splittings

Fitting, socle, HallC3×C11×C37 ⋊ C4×C5
derived, HallC11×C37 ⋊ C3×C4×C5
HallC3×C37×C11⋊C5 ⋊ C4
HallC3×C11⋊#3866 ⋊ C5
HallC37×C11⋊C5 ⋊ C3×C4
HallC11⋊#3866 ⋊ C3×C5
HallC3×C11⋊C5 ⋊ #3866
HallC3×C37 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3×#3866
SylowC37 ⋊ C3×Dic11⋊C5
HallC3×C11 ⋊ C5×#3866
SylowC11 ⋊ C3×C5×#3866

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊C5)⋊#3866
commutator, hypocenterC11×C37C3×C4×C5
FrattiniC1G
Fitting, socleC3×C11×C37C4×C5
prime radicalC3×C11⋊C5×D37C2
cosocleC11×D37C2×C3×C5
LCSG ▷ C11×C37
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1221

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 44);