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C7×#17984460 #44525896

order30940
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#17984460

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C4
derived, HallC5×C13×C17 ⋊ C4×C7
HallC7×C13×C17 ⋊ AGL(1,𝔽5)
HallC5×C7×C17 ⋊ #261
HallC5×C7×C13 ⋊ #595
HallC13×C17 ⋊ C7×AGL(1,𝔽5)
HallC7×C17 ⋊ #63121
HallC7×C13 ⋊ #66775
HallC5×C17 ⋊ C7×#261
HallC5×C13 ⋊ C7×#595
HallC5×C7 ⋊ #11725131
SylowC17 ⋊ C7×#63121
SylowC13 ⋊ C7×#66775
SylowC5 ⋊ C7×#11725131

Subgroups

subgroupG/H
center, hypercenterC7#17984460
commutator, hypocenterC5×C13×C17C4×C7
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC7×D1105C2
cosocleD1105C2×C7
LCSG ▷ C5×C13×C17
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 46);