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C52×C3⋊(C7⋊#595) #49087923

order35700
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×C3⋊(C7⋊#595)
unambiguous semidirect productC3⋊(C52×C7⋊#595)
unambiguous semidirect productC7⋊(C52×C3⋊#595)

Splittings

Fitting, socle, HallC3×C52×C7×C17 ⋊ C4
derived, HallC3×C7×C17 ⋊ C4×C52
HallC52×C7×C17 ⋊ Dic3
HallC3×C52×C17 ⋊ Dic7
HallC3×C52×C7 ⋊ #595
HallC52×C17 ⋊ Dic21
HallC52×C7 ⋊ C3⋊#595
HallC7×C17 ⋊ C52×Dic3
HallC3×C52 ⋊ C7⋊#595
HallC3×C17 ⋊ C52×Dic7
HallC3×C7 ⋊ C52×#595
SylowC17 ⋊ C52×Dic21
SylowC7 ⋊ C52×C3⋊#595
SylowC3 ⋊ C52×C7⋊#595

Subgroups

subgroupG/H
center, hypercenterC52C3⋊(C7⋊#595)
commutator, hypocenterC3×C7×C17C4×C52
FrattiniC1G
Fitting, socleC3×C52×C7×C17C4
prime radicalC3×C52×C7×D17C2
cosocleC3×C7×D17C2×C52
LCSG ▷ C3×C7×C17
UCSC1 ◁ C52

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8925

Conjugacy classes & character table

2700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 397);