Finite Group Databasebeta

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C11×(C49⋊C3)⋊Dic5 #44568330

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×(C49⋊C3)⋊Dic5
unambiguous semidirect product(C49⋊C3)⋊(C11×Dic5)
unambiguous semidirect productDic245⋊(C3×C11)
unambiguous semidirect product(C11×Dic245)⋊C3

Splittings

derived, HallC5×C49 ⋊ C3×C4×C11
HallC11×Dic245 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C4
HallC5×C11×C49 ⋊ C3×C4
HallC11×C49⋊C3 ⋊ Dic5
HallDic245 ⋊ C3×C11
HallC5×C49⋊C3 ⋊ C4×C11
HallC11×C49 ⋊ C3×Dic5
HallC49⋊C3 ⋊ C11×Dic5
HallC5×C11 ⋊ (C49⋊C3)⋊C4
SylowC49 ⋊ C3×C11×Dic5
SylowC5 ⋊ C11×(C49⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊(D49⋊C3)
commutator, hypocenterC5×C49C3×C4×C11
FrattiniC2×C7C11×C5⋊AGL(1,𝔽7)
FittingC2×C5×C11×C49C2×C3
socleC2×C5×C7×C11AGL(1,𝔽7)
prime radicalC2×C5×C11×C49⋊C3C2
cosocleC2×C5×C49C2×C3×C11
LCSG ▷ C5×C49
UCSC1 ◁ C2×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10780

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 32);