Finite Group Databasebeta

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C13×C7⋊#66772 #44525931

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

Aliases

direct productC13×C7⋊#66772
unambiguous semidirect productC7⋊(C13×#66772)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C4
derived, HallC5×C7×C17 ⋊ C4×C13
HallC7×C13×C17 ⋊ Dic5
HallC5×C13×C17 ⋊ Dic7
HallC5×C7×C13 ⋊ #595
HallC13×C17 ⋊ Dic35
HallC7×C17 ⋊ C13×Dic5
HallC7×C13 ⋊ #66772
HallC5×C17 ⋊ C13×Dic7
HallC5×C13 ⋊ C7⋊#595
HallC5×C7 ⋊ C13×#595
SylowC17 ⋊ C13×Dic35
SylowC7 ⋊ C13×#66772
SylowC5 ⋊ C13×C7⋊#595

Subgroups

subgroupG/H
center, hypercenterC13C7⋊#66772
commutator, hypocenterC5×C7×C17C4×C13
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC5×C7×C13×D17C2
cosocleC5×C7×D17C2×C13
LCSG ▷ C5×C7×C17
UCSC1 ◁ C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

2314 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 81);