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C37×C3⋊(C11⋊AGL(1,𝔽5)) #37567602

order24420
automorphism?
homologyAbelianization (H1) = C4×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×C3⋊(C11⋊AGL(1,𝔽5))
unambiguous semidirect productC3⋊(C37×C11⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C37×ΓL(1,𝔽16))

Splittings

Fitting, socle, HallC3×C5×C11×C37 ⋊ C4
derived, HallC3×C5×C11 ⋊ C4×C37
HallC5×C11×C37 ⋊ Dic3
HallC3×C11×C37 ⋊ AGL(1,𝔽5)
HallC3×C5×C37 ⋊ Dic11
HallC11×C37 ⋊ ΓL(1,𝔽16)
HallC5×C37 ⋊ Dic33
HallC3×C37 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ Dic3×C37
HallC3×C11 ⋊ AGL(1,𝔽5)×C37
HallC3×C5 ⋊ C37×Dic11
SylowC11 ⋊ C37×ΓL(1,𝔽16)
SylowC5 ⋊ C37×Dic33
SylowC3 ⋊ C37×C11⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC37C3⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC3×C5×C11C4×C37
FrattiniC1G
Fitting, socleC3×C5×C11×C37C4
prime radicalC3×D5×C11×C37C2
cosocleC3×D5×C11C2×C37
LCSG ▷ C3×C5×C11
UCSC1 ◁ C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

2553 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 123);