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C7×D13×C19⋊C3 #23780552

order10374
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D13×C19⋊C3

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C3
derived, HallC13×C19 ⋊ C2×C3×C7
HallC7×C13×C19⋊C3 ⋊ C2
HallC7×C19×D13 ⋊ C3
HallC13×C19⋊C3 ⋊ C2×C7
HallC19×D13 ⋊ C3×C7
HallC7×C19 ⋊ C3×D13
HallC7×C13 ⋊ C2×C19⋊C3
SylowC19 ⋊ C3×C7×D13
SylowC13 ⋊ C2×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D13×C19⋊C3
commutator, cosocle, hypocenterC13×C19C2×C3×C7
FrattiniC1G
Fitting, socleC7×C13×C19C2×C3
LCSG ▷ C13×C19
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

504 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×(C19⋊C3)⋊#261, C7×#261×C19⋊C3, C7×D13×D19⋊C3, …
maximal normal subgroup ofC7×(C19⋊C3)⋊#261, C7×#261×C19⋊C3, C7×D13×D19⋊C3, …
maximal quotient ofC7×Dic13×C19⋊C3, C2×C7×D13×C19⋊C3, C7×D13×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 43);