Finite Group Databasebeta

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C17×Dic455 #44525865

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

Aliases

direct productC17×Dic455
unambiguous semidirect productC7⋊(C17×Dic65)

Splittings

derived, HallC5×C7×C13 ⋊ C4×C17
HallC5×C7×C13×C17 ⋊ C4
HallC7×C13×C17 ⋊ Dic5
HallC5×C13×C17 ⋊ Dic7
HallC5×C7×C17 ⋊ Dic13
HallC13×C17 ⋊ Dic35
HallC7×C17 ⋊ Dic65
HallC7×C13 ⋊ C17×Dic5
HallC5×C17 ⋊ Dic91
HallC5×C13 ⋊ C17×Dic7
HallC5×C7 ⋊ C17×Dic13
SylowC13 ⋊ C17×Dic35
SylowC7 ⋊ C17×Dic65
SylowC5 ⋊ C17×Dic91

Subgroups

subgroupG/H
center, hypercenterC2×C17D455
commutator, hypocenterC5×C7×C13C4×C17
FrattiniC2C17×D455
Fitting, socle, prime radicalC2×C5×C7×C13×C17C2
cosocleC2×C5×C7×C13C2×C17
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30940

Conjugacy classes & character table

7786 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 15);