Finite Group Databasebeta

← Prev (#36345322) Next (#36345324) →

C5×D32×C112 #36345323

order21780
automorphism?
homologyAbelianization (H1) = C22×C5×C112 · Schur multiplier (H2) = C2×C11

Aliases

direct productC5×D32×C112
unambiguous semidirect product(C3×D3)⋊(C2×C5×C112)
unambiguous semidirect product(C3⋊D3)⋊(C2×C5×C112)

Splittings

Fitting, socle, HallC32×C5×C112 ⋊ C22
derived, SylowC32 ⋊ C22×C5×C112
HallC32×C112 ⋊ C22×C5
HallC32×C5 ⋊ C22×C112

Subgroups

subgroupG/H
center, hypercenterC5×C112D32
commutator, cosocle, hypocenterC32C22×C5×C112
FrattiniC1G
Fitting, socleC32×C5×C112C22
LCSG ▷ C32
UCSC1 ◁ C5×C112

616 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5445 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 672);