Finite Group Databasebeta

← Prev (#24924248) Next (#24924250) →

C32×C5×C7×D17 #24924249

order10710
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C7×D17
unambiguous semidirect productC17⋊(C2×C32×C5×C7)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C2
derived, SylowC17 ⋊ C2×C32×C5×C7
HallC32×C7×C17 ⋊ C2×C5
HallC32×C5×C17 ⋊ C2×C7
HallC5×C7×C17 ⋊ C2×C32
HallC32×C17 ⋊ C2×C5×C7
HallC7×C17 ⋊ C2×C32×C5
HallC5×C17 ⋊ C2×C32×C7

Subgroups

subgroupG/H
center, hypercenterC32×C5×C7D17
commutator, cosocle, hypocenterC17C2×C32×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C2
LCSG ▷ C17
UCSC1 ◁ C32×C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×C7×#595, C32×C5×C7⋊#595, C32×C5×D7×D17, …
maximal normal subgroup ofC32×C5×C7×#595, C32×C5×C7⋊#595, C32×C5×D7×D17, …
maximal quotient ofC32×C5×C7×Dic17, C2×C32×C5×C7×D17

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 64);