Finite Group Databasebeta

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C5×C13×C7⋊#595 #44525875

order30940
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×C7⋊#595
unambiguous semidirect productC7⋊(C5×C13×#595)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C13C7⋊#595
commutator, hypocenterC7×C17C4×C5×C13
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC5×C7×C13×D17C2
cosocleC7×D17C2×C5×C13
LCSG ▷ C7×C17
UCSC1 ◁ C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

2470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 25);