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C2×C7×D377 #24902244

order10556
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D377
unambiguous semidirect product(C2×C13)⋊(C7×D29)

Splittings

Fitting, socleC2×C7×C13×C29 ⋊ C2
derived, HallC13×C29 ⋊ C22×C7
HallC7×C13×C29 ⋊ C22
HallC7×C29 ⋊ C2×D13
HallC7×C13 ⋊ C2×D29
SylowC29 ⋊ C2×C7×D13
SylowC13 ⋊ C2×C7×D29

Subgroups

subgroupG/H
center, hypercenterC2×C7D377
commutator, cosocle, hypocenterC13×C29C22×C7
FrattiniC1G
Fitting, socleC2×C7×C13×C29C2
LCSG ▷ C13×C29
UCSC1 ◁ C2×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2660 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C29⋊(D13⋊C3), C2×C29⋊#10587716, C2×C29⋊#10587717, …
maximal normal subgroup ofC2×C7×C29⋊(D13⋊C3), C2×C29⋊#10587716, C2×C29⋊#10587717, …
maximal quotient ofD3×C7×D377, C2×C3×C7×D377, C2×C7×D1131

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10556, 48);