Finite Group Databasebeta

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C5×C11⋊(Dic37⋊C3) #37567508

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

Aliases

direct productC5×C11⋊(Dic37⋊C3)
unambiguous semidirect product(C5×Dic407)⋊C3

Splittings

derived, HallC11×C37 ⋊ C3×C4×C5
HallC5×Dic407 ⋊ C3
HallC5×C11×C37⋊C3 ⋊ C4
HallC5×C11×C37 ⋊ C3×C4
HallDic407 ⋊ C3×C5
HallC11×C37⋊C3 ⋊ C4×C5
HallC5×C37⋊C3 ⋊ Dic11
HallC5×C37 ⋊ C3×Dic11
HallC37⋊C3 ⋊ C5×Dic11
HallC5×C11 ⋊ Dic37⋊C3
SylowC37 ⋊ C3×C5×Dic11
SylowC11 ⋊ C5×Dic37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊(D37⋊C3)
commutator, hypocenterC11×C37C3×C4×C5
FrattiniC2C5×C11⋊(D37⋊C3)
Fitting, socleC2×C5×C11×C37C2×C3
prime radicalC2×C5×C11×C37⋊C3C2
cosocleC2×C11×C37C2×C3×C5
LCSG ▷ C11×C37
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8140

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 29);