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D5×C211⋊C5 #24902167

order10550
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD5×C211⋊C5
unambiguous semidirect productC5⋊(C2×C211⋊C5)
unambiguous semidirect product(D5×C211)⋊C5

Splittings

Fitting, socle, derivedC5×C211 ⋊ C2×C5
HallC5×C211⋊C5 ⋊ C2
SylowC211 ⋊ C5×D5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C211C2×C5
LCSG ▷ C5×C211
UCSC1

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C211⋊C5)⋊AGL(1,𝔽5), AGL(1,𝔽5)×C211⋊C5, D5×D211⋊C5, …
maximal normal subgroup of(C211⋊C5)⋊AGL(1,𝔽5), AGL(1,𝔽5)×C211⋊C5, D5×D211⋊C5, …
maximal quotient ofDic5×C211⋊C5, C2×D5×C211⋊C5, C3×D5×C211⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10550, 10);