Finite Group Databasebeta

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C7×C13×C17×AGL(1,𝔽5) #44525887

order30940
automorphism?
homologyAbelianization (H1) = C4×C7×C13×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13×C17×AGL(1,𝔽5)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C4
derived, SylowC5 ⋊ C4×C7×C13×C17
HallC5×C13×C17 ⋊ C4×C7
HallC5×C7×C17 ⋊ C4×C13
HallC5×C7×C13 ⋊ C4×C17
HallC5×C17 ⋊ C4×C7×C13
HallC5×C13 ⋊ C4×C7×C17
HallC5×C7 ⋊ C4×C13×C17

Subgroups

subgroupG/H
center, hypercenterC7×C13×C17AGL(1,𝔽5)
commutator, hypocenterC5C4×C7×C13×C17
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC7×D5×C13×C17C2
cosocleD5C2×C7×C13×C17
LCSG ▷ C5
UCSC1 ◁ C7×C13×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

7735 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 37);