Finite Group Databasebeta

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C7×C13×#66774 #44525890

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

Aliases

direct productC7×C13×#66774

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C4
derived, HallC5×C17 ⋊ C4×C7×C13
HallC7×C13×C17 ⋊ AGL(1,𝔽5)
HallC5×C13×C17 ⋊ C4×C7
HallC5×C7×C17 ⋊ C4×C13
HallC5×C7×C13 ⋊ Dic17
HallC13×C17 ⋊ C7×AGL(1,𝔽5)
HallC7×C17 ⋊ C13×AGL(1,𝔽5)
HallC5×C13 ⋊ C7×Dic17
HallC5×C7 ⋊ C13×Dic17
SylowC17 ⋊ C7×C13×AGL(1,𝔽5)
SylowC5 ⋊ C7×C13×Dic17

Subgroups

subgroupG/H
center, hypercenterC7×C13#66774
commutator, hypocenterC5×C17C4×C7×C13
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC7×D5×C13×C17C2
cosocleD5×C17C2×C7×C13
LCSG ▷ C5×C17
UCSC1 ◁ C7×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

3367 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 40);