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C7×(C11⋊C5)⋊Dic13 #34093443

order20020
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×(C11⋊C5)⋊Dic13
unambiguous semidirect product(C11⋊C5)⋊(C7×Dic13)
unambiguous semidirect productDic143⋊(C5×C7)
unambiguous semidirect product(C7×Dic143)⋊C5

Splittings

derived, HallC11×C13 ⋊ C4×C5×C7
HallC7×C13×C11⋊C5 ⋊ C4
HallC7×Dic143 ⋊ C5
HallC7×C11×C13 ⋊ C4×C5
HallC13×C11⋊C5 ⋊ C4×C7
HallDic143 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ Dic13
HallC7×C13 ⋊ Dic11⋊C5
HallC7×C11 ⋊ C5×Dic13
HallC11⋊C5 ⋊ C7×Dic13
SylowC13 ⋊ C7×Dic11⋊C5
SylowC11 ⋊ C5×C7×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C7C13⋊AGL(1,𝔽11)
commutator, hypocenterC11×C13C4×C5×C7
FrattiniC2C7×C13⋊AGL(1,𝔽11)
Fitting, socleC2×C7×C11×C13C2×C5
prime radicalC2×C7×C13×C11⋊C5C2
cosocleC2×C11×C13C2×C5×C7
LCSG ▷ C11×C13
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 4004

A minimal faithful permutation representation — 2 generators on 35 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 20);