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C11⋊#11760384 #26040519

order11550
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

unambiguous semidirect productC11⋊#11760384

Splittings

Fitting, socle, derived, HallC52×C7×C11 ⋊ C2×C3
HallC7×C11×C52⋊C3 ⋊ C2
HallC5⋊D385 ⋊ C3
HallC11×C52⋊C3 ⋊ D7
HallC7×C52⋊C3 ⋊ D11
HallC52×C11 ⋊ C3×D7
HallC52×C7 ⋊ C3×D11
HallC7×C11 ⋊ (C5⋊D5)⋊C3
HallC52⋊C3 ⋊ D77
SylowC52 ⋊ C3×D77
SylowC11 ⋊ #11760384
SylowC7 ⋊ C11⋊((C5⋊D5)⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C7×C11C2×C3
LCSG ▷ C52×C7×C11
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,5^2,7,11|c^a=c^4,d^a=d^4,e^a=e^6,f^a=f^10,c^b=cd,d^b=c^2d^3

Conjugacy classes & character table

428 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#3874⋊D77, #37528478, D7×C11⋊((C5⋊D5)⋊C3), …
maximal normal subgroup of#3874⋊D77, #37528478, D7×C11⋊((C5⋊D5)⋊C3), …
maximal quotient ofC11⋊#14523572, C2×C11⋊#11760384, C11⋊#15691245, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 83);