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C3×AGL(1,𝔽5)×C112⋊C3 #36345183

order21780
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C11

Aliases

direct productC3×AGL(1,𝔽5)×C112⋊C3
unambiguous semidirect product(C112×AGL(1,𝔽5))⋊C32
unambiguous semidirect product(C3×C112×AGL(1,𝔽5))⋊C3

Splittings

Fitting, socleC3×C5×C112 ⋊ C3×C4
derived, HallC5×C112 ⋊ C32×C4
HallC3×C5×C112⋊C3 ⋊ C4
HallC112×AGL(1,𝔽5) ⋊ C32
SylowC112 ⋊ C32×AGL(1,𝔽5)
SylowC5 ⋊ C3×C4×C112⋊C3

Subgroups

subgroupG/H
center, hypercenterC3AGL(1,𝔽5)×C112⋊C3
commutator, hypocenterC5×C112C32×C4
FrattiniC1G
Fitting, socleC3×C5×C112C3×C4
prime radicalC3×D5×C112⋊C3C2
cosocleD5×C112C2×C32
LCSG ▷ C5×C112
UCSC1 ◁ C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

645 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 532);