Finite Group Databasebeta

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D55×#3862 #30633562

order16170
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C7

Aliases

direct productD55×#3862
unambiguous semidirect productC5⋊(D11×#3862)
unambiguous semidirect productC11⋊(D5×#3862)

Splittings

Fitting, socle, derived, HallC5×C72×C11 ⋊ C2×C3
HallC5×C11×#3862 ⋊ C2
HallC72×D55 ⋊ C3
HallC11×#3862 ⋊ D5
HallC5×#3862 ⋊ D11
HallC72×C11 ⋊ C3×D5
HallC5×C72 ⋊ C3×D11
HallC5×C11 ⋊ C2×#3862
SylowC72 ⋊ C3×D55
SylowC11 ⋊ D5×#3862
SylowC5 ⋊ D11×#3862

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C11C2×C3
LCSG ▷ C5×C72×C11
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1155

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD55×#64418, D55⋊#64418, D55×#64422, …
maximal normal subgroup ofD55×#64418, D55⋊#64418, D55×#64422, …
maximal quotient of#3862×Dic55, C2×D55×#3862

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 107);