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C7×C22⋊(C103⋊C3) #22575779

order8652
automorphism?
homologyAbelianization (H1) = C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×C22⋊(C103⋊C3)
unambiguous semidirect productC22⋊(C7×C103⋊C3)
unambiguous semidirect productC103⋊(C7×A4)

Splittings

Fitting, socle, HallC22×C7×C103 ⋊ C3
derived, HallC22×C103 ⋊ C3×C7
HallC7×C103 ⋊ A4
SylowC103 ⋊ C7×A4
HallC22×C7 ⋊ C103⋊C3
SylowC22 ⋊ C7×C103⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C22⋊(C103⋊C3)
commutator, hypocenterC22×C103C3×C7
FrattiniC1G
Fitting, socleC22×C7×C103C3
LCSG ▷ C22×C103
UCSC1 ◁ C7

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

980 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×A4×C103⋊C3, ΓL(1,𝔽8)×C22⋊(C103⋊C3), #14524189⋊A4, …
maximal normal subgroup ofC7×A4×C103⋊C3, ΓL(1,𝔽8)×C22⋊(C103⋊C3), #14524189⋊A4, …
maximal quotient ofC7×C22⋊(C103⋊C9), C3×C7×C22⋊(C103⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8652, 52);