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(C3⋊D3)⋊C3×C11⋊C5 #72228754

order2970
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C3

Aliases

direct product(C3⋊D3)⋊C3×C11⋊C5

Splittings

Fitting, HallC11×H(3,𝔽3) ⋊ C2×C5
derivedC32×C11 ⋊ C2×C3×C5
HallH(3,𝔽3)×C11⋊C5 ⋊ C2
HallC11×(C3⋊D3)⋊C3 ⋊ C5
SylowH(3,𝔽3) ⋊ C2×C11⋊C5
SylowC11 ⋊ C5×(C3⋊D3)⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC32×C11C2×C3×C5
FrattiniC3C3×D3×C11⋊C5
FittingC11×H(3,𝔽3)C2×C5
socleC3×C11C3×C5×D3
LCSG ▷ C32×C11
UCSC1

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 99

A minimal faithful permutation representation — 2 generators on 20 points:

(2,7,9,4,5,8)(3,6)(11,12,14,17,16)(13,15,19,20,18);(1,2,4)(3,5,8)(6,9,7)(10,11,13,16,12,14,18,20,15,17,19)

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11⋊C5×PSU(3,𝔽2)⋊C3, (C3⋊D3)⋊C3×AGL(1,𝔽11), C11⋊C5×((C3⋊D3)⋊C3)⋊C2, …
maximal normal subgroup of(C3⋊D3)⋊C3×AGL(1,𝔽11), C11⋊C5×((C3⋊D3)⋊C3)⋊C2, #72259120

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((2,7,9,4,5,8)(3,6)(11,12,14,17,16)(13,15,19,20,18), (1,2,4)(3,5,8)(6,9,7)(10,11,13,16,12,14,18,20,15,17,19));