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C7×#92150⋊C3 #23779014

order10164
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C11

Aliases

direct productC7×#92150⋊C3
unambiguous semidirect product#92150⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C112 ⋊ C3×C4
derived, SylowC112 ⋊ C3×C4×C7
HallC7×#92150 ⋊ C3
HallC7×C112⋊C3 ⋊ C4
Hall#92150 ⋊ C3×C7
HallC112⋊C3 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC7#92150⋊C3
commutator, hypocenterC112C3×C4×C7
FrattiniC1G
Fitting, socleC7×C112C3×C4
prime radicalC7×(C11⋊D11)⋊C3C2
cosocleC11⋊D11C2×C3×C7
LCSG ▷ C112
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×#92150⋊C3, C3×C7×#92150⋊C3, C7×C3⋊(#92150⋊C3)
maximal normal subgroup ofΓL(1,𝔽8)×#92150⋊C3, C3×C7×#92150⋊C3
maximal quotient ofC7×#92150⋊C9, C3×C7×#92150⋊C3, C7×C3⋊(#92150⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10164, 66);