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C37⋊C3×C11⋊AGL(1,𝔽5) #37567547

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

Aliases

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

Splittings

Fitting, socle, derived, HallC5×C11×C37 ⋊ C3×C4
HallC37×C11⋊AGL(1,𝔽5) ⋊ C3
HallC5×C11×C37⋊C3 ⋊ C4
HallC11×C37⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C37⋊C3 ⋊ Dic11
HallC11×C37 ⋊ C3×AGL(1,𝔽5)
HallC5×C37 ⋊ C3×Dic11
HallC5×C11 ⋊ C4×C37⋊C3
SylowC37 ⋊ C3×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ AGL(1,𝔽5)×C37⋊C3
SylowC5 ⋊ Dic11×C37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C11×C37C3×C4
prime radicalD5×C11×C37⋊C3C2
cosocleD5×C11×C37C2×C3
LCSG ▷ C5×C11×C37
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2035

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 68);