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C5×C7⋊#11725131 #44525879

order30940
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7⋊#11725131
unambiguous semidirect productC7⋊(C5×#11725131)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C4
derived, HallC7×C13×C17 ⋊ C4×C5
HallC5×C13×C17 ⋊ Dic7
HallC5×C7×C17 ⋊ #261
HallC5×C7×C13 ⋊ #595
HallC13×C17 ⋊ C5×Dic7
HallC7×C17 ⋊ C5×#261
HallC7×C13 ⋊ C5×#595
HallC5×C17 ⋊ C7⋊#261
HallC5×C13 ⋊ C7⋊#595
HallC5×C7 ⋊ #11725131
SylowC17 ⋊ C5×C7⋊#261
SylowC13 ⋊ C5×C7⋊#595
SylowC7 ⋊ C5×#11725131

Subgroups

subgroupG/H
center, hypercenterC5C7⋊#11725131
commutator, hypocenterC7×C13×C17C4×C5
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC5×C7×D221C2
cosocleC7×D221C2×C5
LCSG ▷ C7×C13×C17
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

1975 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 29);