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C49⋊(Dic11⋊C5) #24924691

order10780
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC49⋊(Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊Dic49
unambiguous semidirect productDic539⋊C5

Splittings

derived, HallC11×C49 ⋊ C4×C5
HallC49×C11⋊C5 ⋊ C4
HallDic539 ⋊ C5
HallC11⋊C5 ⋊ Dic49
SylowC49 ⋊ Dic11⋊C5
SylowC11 ⋊ C5×Dic49

Subgroups

subgroupG/H
center, hypercenterC2C49⋊AGL(1,𝔽11)
commutator, hypocenterC11×C49C4×C5
FrattiniC2×C7C7⋊AGL(1,𝔽11)
Fitting, cosocleC2×C11×C49C2×C5
socleC2×C7×C11C5×D7
prime radicalC2×C7×C11⋊C5D7
LCSG ▷ C11×C49
UCSC1 ◁ C2

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

358 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C49⋊(Dic11⋊C5), C3⋊(C49⋊(Dic11⋊C5)), (C11⋊C5)⋊((C49⋊C3)⋊C4)
maximal normal subgroup ofC3×C49⋊(Dic11⋊C5), (C11⋊C5)⋊((C49⋊C3)⋊C4)
maximal quotient ofC3×C49⋊(Dic11⋊C5), C3⋊(C49⋊(Dic11⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 4);