Finite Group Databasebeta

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C7×#15690395 #36339429

order21420
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×#15690395

Splittings

Fitting, socle, HallC32×C5×C7×C17 ⋊ C4
derived, HallC32×C5×C17 ⋊ C4×C7
HallC32×C7×C17 ⋊ Dic5
HallC5×C7×C17 ⋊ #157
HallC32×C5×C7 ⋊ Dic17
HallC32×C17 ⋊ C7×Dic5
HallC7×C17 ⋊ #4379
HallC5×C17 ⋊ C7×#157
HallC32×C7 ⋊ Dic85
HallC32×C5 ⋊ C7×Dic17
HallC5×C7 ⋊ #10597480
SylowC17 ⋊ C7×#4379
SylowC32 ⋊ C7×Dic85
SylowC5 ⋊ C7×#10597480

Subgroups

subgroupG/H
center, hypercenterC7#15690395
commutator, hypocenterC32×C5×C17C4×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C17C4
prime radicalC5×C7×C17×C3⋊D3C2
cosocleC5×C17×C3⋊D3C2×C7
LCSG ▷ C32×C5×C17
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3570

Conjugacy classes & character table

1806 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 261);