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C3×C37×C11⋊AGL(1,𝔽5) #37567578

order24420
automorphism?
homologyAbelianization (H1) = C3×C4×C37 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C5×C11×C37 ⋊ C4
derived, HallC5×C11 ⋊ C3×C4×C37
HallC5×C11×C37 ⋊ C3×C4
HallC3×C11×C37 ⋊ AGL(1,𝔽5)
HallC3×C5×C37 ⋊ Dic11
HallC11×C37 ⋊ C3×AGL(1,𝔽5)
HallC5×C37 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ C4×C37
HallC3×C11 ⋊ AGL(1,𝔽5)×C37
HallC3×C5 ⋊ C37×Dic11
SylowC11 ⋊ C3×AGL(1,𝔽5)×C37
SylowC5 ⋊ C3×C37×Dic11

Subgroups

subgroupG/H
center, hypercenterC3×C37C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C4×C37
FrattiniC1G
Fitting, socleC3×C5×C11×C37C4
prime radicalC3×D5×C11×C37C2
cosocleD5×C11C2×C3×C37
LCSG ▷ C5×C11
UCSC1 ◁ C3×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

2775 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 99);