Finite Group Databasebeta

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C5×C17×C7⋊#261 #44525877

order30940
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×C7⋊#261
unambiguous semidirect productC7⋊(C5×C17×#261)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C17C7⋊#261
commutator, hypocenterC7×C13C4×C5×C17
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC5×C7×C17×D13C2
cosocleC7×D13C2×C5×C17
LCSG ▷ C7×C13
UCSC1 ◁ C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

2635 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 27);