Finite Group Databasebeta

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C32×C7×D5×C17 #24924246

order10710
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C32×C7×C17 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×D5×C17
unambiguous semidirect productC5⋊(C2×C32×C7×C17)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derived, SylowC5 ⋊ C2×C32×C7×C17
HallC32×C5×C17 ⋊ C2×C7
HallC5×C7×C17 ⋊ C2×C32
HallC32×C5×C7 ⋊ C2×C17
HallC5×C17 ⋊ C2×C32×C7
HallC32×C5 ⋊ C2×C7×C17
HallC5×C7 ⋊ C2×C32×C17

Subgroups

subgroupG/H
center, hypercenterC32×C7×C17D5
commutator, cosocle, hypocenterC5C2×C32×C7×C17
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C5
UCSC1 ◁ C32×C7×C17

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4284 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C7×C17×AGL(1,𝔽5), C32×C7×#66774, C32×C17×C7⋊AGL(1,𝔽5), …
maximal normal subgroup ofC32×C7×C17×AGL(1,𝔽5), C32×C7×#66774, C32×C17×C7⋊AGL(1,𝔽5), …
maximal quotient ofC32×C7×C17×Dic5, C2×C32×C7×D5×C17

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 61);