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C32×C7⋊#66774 #36339443

order21420
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7⋊#66774

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C4
derived, HallC5×C7×C17 ⋊ C32×C4
HallC32×C7×C17 ⋊ AGL(1,𝔽5)
HallC32×C5×C17 ⋊ Dic7
HallC32×C5×C7 ⋊ Dic17
HallC32×C17 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C17 ⋊ C32×AGL(1,𝔽5)
HallC5×C17 ⋊ C32×Dic7
HallC32×C7 ⋊ #66774
HallC32×C5 ⋊ Dic119
HallC5×C7 ⋊ C32×Dic17
SylowC17 ⋊ C32×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C32×#66774
SylowC5 ⋊ C32×Dic119

Subgroups

subgroupG/H
center, hypercenterC32C7⋊#66774
commutator, hypocenterC5×C7×C17C32×C4
FrattiniC1G
Fitting, socleC32×C5×C7×C17C4
prime radicalC32×C7×D5×C17C2
cosocleC7×D5×C17C2×C32
LCSG ▷ C5×C7×C17
UCSC1 ◁ C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

2169 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 275);