Finite Group Databasebeta

← Prev (#50303620) Next (#50303622) →

C7×#19129703 #50303621

order38220
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#19129703

Splittings

derivedC5×C7×C13 ⋊ C3×C4×C7
HallC7×Dic455 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C4
HallC5×C72×C13 ⋊ C3×C4
HallC72×C13⋊C3 ⋊ Dic5
HallC72×C13 ⋊ C3×Dic5
HallC5×C72 ⋊ Dic13⋊C3
HallC5×C13⋊C3 ⋊ C7×Dic7
HallC5×C13 ⋊ C3×C7×Dic7
SylowC72 ⋊ Dic65⋊C3
HallC13⋊C3 ⋊ C7×Dic35
SylowC13 ⋊ C3×C7×Dic35
SylowC5 ⋊ C7×#11763955

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊((C13⋊C3)⋊D7)
commutator, hypocenterC5×C7×C13C3×C4×C7
FrattiniC2C7×C5⋊((C13⋊C3)⋊D7)
Fitting, socleC2×C5×C72×C13C2×C3
prime radicalC2×C5×C72×C13⋊C3C2
cosocleC2×C5×C7×C13C2×C3×C7
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C7

144 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1820

Conjugacy classes & character table

1778 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 307);