Finite Group Databasebeta

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C32×D5×C112 #24926211

order10890
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C32×C112 · Schur multiplier (H2) = C3×C11

Aliases

direct productC32×D5×C112
unambiguous semidirect productC5⋊(C2×C32×C112)

Splittings

Fitting, socle, HallC32×C5×C112 ⋊ C2
derived, SylowC5 ⋊ C2×C32×C112
HallC5×C112 ⋊ C2×C32
HallC32×C5 ⋊ C2×C112

Subgroups

subgroupG/H
center, hypercenterC32×C112D5
commutator, cosocle, hypocenterC5C2×C32×C112
FrattiniC1G
Fitting, socleC32×C5×C112C2
LCSG ▷ C5
UCSC1 ◁ C32×C112

336 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4356 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C112×AGL(1,𝔽5), C32×C11×C11⋊AGL(1,𝔽5), C32×C11⋊(C11⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC32×C112×AGL(1,𝔽5), C32×C11×C11⋊AGL(1,𝔽5), C32×C11⋊(C11⋊AGL(1,𝔽5)), …
maximal quotient ofC32×C112×Dic5, C2×C32×D5×C112

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 160);