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C17×C7⋊#63120 #44525915

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

Aliases

direct productC17×C7⋊#63120
unambiguous semidirect productC7⋊(C17×#63120)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C4
derived, HallC5×C7×C13 ⋊ C4×C17
HallC7×C13×C17 ⋊ AGL(1,𝔽5)
HallC5×C13×C17 ⋊ Dic7
HallC5×C7×C17 ⋊ Dic13
HallC13×C17 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C17 ⋊ #63120
HallC7×C13 ⋊ C17×AGL(1,𝔽5)
HallC5×C17 ⋊ Dic91
HallC5×C13 ⋊ C17×Dic7
HallC5×C7 ⋊ C17×Dic13
SylowC13 ⋊ C17×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C17×#63120
SylowC5 ⋊ C17×Dic91

Subgroups

subgroupG/H
center, hypercenterC17C7⋊#63120
commutator, hypocenterC5×C7×C13C4×C17
FrattiniC1G
Fitting, socleC5×C7×C13×C17C4
prime radicalC7×D5×C13×C17C2
cosocleC7×D5×C13C2×C17
LCSG ▷ C5×C7×C13
UCSC1 ◁ C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

3145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 65);