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D11×D455 #34093508

order20020
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD11×D455
unambiguous semidirect product(C5×D11)⋊D91
unambiguous semidirect product(C7×D11)⋊D65
unambiguous semidirect product(C13×D11)⋊D35

Splittings

Fitting, socle, derived, HallC5×C7×C11×C13 ⋊ C22
HallC7×C11×C13 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×D7
HallC5×C7×C13 ⋊ C2×D11
HallC5×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×D35
HallC7×C13 ⋊ D5×D11
HallC7×C11 ⋊ C2×D65
HallC5×C13 ⋊ D7×D11
HallC5×C11 ⋊ C2×D91
HallC5×C7 ⋊ D11×D13
SylowC13 ⋊ D11×D35
SylowC11 ⋊ C2×D455
SylowC7 ⋊ D11×D65
SylowC5 ⋊ D11×D91

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C11×C13C22
LCSG ▷ C5×C7×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 5005

A minimal faithful permutation representation — 2 generators on 36 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16)(17,18)(19,20)(22,23)(24,25)(26,27,29,31,33,35,36,34,32,30,28);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,17,19,20,18,16)(21,22,24,25,23)(27,28)(29,30)(31,32)(33,34)(35,36)

Conjugacy classes & character table

1603 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 85);