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C7×#13093364 #23780554

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

Aliases

direct productC7×#13093364

Splittings

Fitting, socle, HallC7×C13×C19 ⋊ C2×C3
derived, HallC13×C19 ⋊ C2×C3×C7
HallC7×#10625202 ⋊ C2
HallC7×C19×D13 ⋊ C3
Hall#10625202 ⋊ C2×C7
HallC19×D13 ⋊ C3×C7
HallC7×D13 ⋊ C19⋊C3
HallC7×C19 ⋊ D13⋊C3
HallC7×C13 ⋊ C2×C19⋊C3
HallD13 ⋊ C7×C19⋊C3
SylowC19 ⋊ C7×D13⋊C3
SylowC13 ⋊ C2×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC7#13093364
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

392 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×#15688300, C7×#15688302, C7×#13093360⋊C2, …
maximal normal subgroup ofC7×#15688300, C7×#15688302, C7×#13093360⋊C2, …
maximal quotient ofC7×#15688283, C2×C7×#13093364, C7×#17984621, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 45);