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C7×#17984466 #44525902

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

Aliases

direct productC7×#17984466

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C4
derived, HallC5×C13×C17 ⋊ C4×C7
HallC7×C13×C17 ⋊ AGL(1,𝔽5)
HallC5×C7×C17 ⋊ Dic13
HallC5×C7×C13 ⋊ Dic17
HallC13×C17 ⋊ C7×AGL(1,𝔽5)
HallC7×C17 ⋊ #63120
HallC7×C13 ⋊ #66774
HallC5×C17 ⋊ C7×Dic13
HallC5×C13 ⋊ C7×Dic17
HallC5×C7 ⋊ Dic221
SylowC17 ⋊ C7×#63120
SylowC13 ⋊ C7×#66774
SylowC5 ⋊ C7×Dic221

Subgroups

subgroupG/H
center, hypercenterC7#17984466
commutator, hypocenterC5×C13×C17C4×C7
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC7×D5×C13×C17C2
cosocleD5×C13×C17C2×C7
LCSG ▷ C5×C13×C17
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

3115 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 52);