Finite Group Databasebeta

← Prev (#24924780) Next (#24924782) →

D55⋊(C7⋊D7) #24924781

order10780
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C7

Aliases

unambiguous semidirect productD55⋊(C7⋊D7)

Splittings

Fitting, socle, derived, HallC5×C72×C11 ⋊ C22
HallC72×C11 ⋊ C2×D5
HallC5×C72 ⋊ C2×D11
HallC5×C11 ⋊ C2×C7⋊D7
SylowC72 ⋊ D5×D11
SylowC11 ⋊ D5×C7⋊D7
SylowC5 ⋊ D11×C7⋊D7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C72×C11C22
LCSG ▷ C5×C72×C11
UCSC1

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,5,7^2,11|d^a=d^6,e^a=e^6,f^a=f^10,c^b=c^4,d^b=d^6,e^b=e^6

Conjugacy classes & character table

724 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD55⋊(ΓL(1,𝔽8)⋊D7), D55⋊#64424, D55⋊#64425, …
maximal normal subgroup ofD55⋊(ΓL(1,𝔽8)⋊D7), D55⋊#64424, D55⋊#64425, …
maximal quotient ofC3×D55⋊(C7⋊D7), #44568884, D55⋊(C3⋊(C7⋊D7)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 94);