Finite Group Databasebeta

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C17×C7⋊#4379 #36339430

order21420
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C3

Aliases

direct productC17×C7⋊#4379
unambiguous semidirect productC7⋊(C17×#4379)

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C4
derived, HallC32×C5×C7 ⋊ C4×C17
HallC32×C7×C17 ⋊ Dic5
HallC32×C5×C17 ⋊ Dic7
HallC5×C7×C17 ⋊ #157
HallC32×C17 ⋊ Dic35
HallC7×C17 ⋊ #4379
HallC5×C17 ⋊ C7⋊#157
HallC32×C7 ⋊ C17×Dic5
HallC32×C5 ⋊ C17×Dic7
HallC5×C7 ⋊ C17×#157
SylowC32 ⋊ C17×Dic35
SylowC7 ⋊ C17×#4379
SylowC5 ⋊ C17×C7⋊#157

Subgroups

subgroupG/H
center, hypercenterC17C7⋊#4379
commutator, hypocenterC32×C5×C7C4×C17
FrattiniC1G
Fitting, socleC32×C5×C7×C17C4
prime radicalC5×C7×C17×C3⋊D3C2
cosocleC5×C7×C3⋊D3C2×C17
LCSG ▷ C32×C5×C7
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3570

Conjugacy classes & character table

1836 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 262);