Finite Group Databasebeta

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C2×C7×#10625202 #23780513

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

Aliases

direct productC2×C7×#10625202

Splittings

Fitting, socle, HallC2×C7×C13×C19 ⋊ C3
derived, HallC13×C19 ⋊ C2×C3×C7
HallC7×C13×C19 ⋊ C2×C3
HallC2×C13×C19 ⋊ C3×C7
HallC2×C7×C19 ⋊ C13⋊C3
HallC2×C7×C13 ⋊ C19⋊C3
HallC7×C19 ⋊ C2×C13⋊C3
HallC7×C13 ⋊ C2×C19⋊C3
HallC2×C19 ⋊ C7×C13⋊C3
HallC2×C13 ⋊ C7×C19⋊C3
SylowC19 ⋊ C2×C7×C13⋊C3
SylowC13 ⋊ C2×C7×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7#10625202
commutator, cosocle, hypocenterC13×C19C2×C3×C7
FrattiniC1G
Fitting, socleC2×C7×C13×C19C3
LCSG ▷ C13×C19
UCSC1 ◁ C2×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C7×#10625202, C7×#15688279, C7×#15688283, …
maximal normal subgroup ofC4×C7×#10625202, C7×#15688279, C7×#15688283, …
maximal quotient ofC4×C7×#10625202, C22×C7×#10625202, C2×C7×#14555735, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 4);