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C7⋊((C11⋊C5)⋊Dic13) #34093447

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

Aliases

unambiguous semidirect productC7⋊((C11⋊C5)⋊Dic13)
unambiguous semidirect product(C11⋊C5)⋊Dic91
unambiguous semidirect productDic1001⋊C5

Splittings

derived, HallC7×C11×C13 ⋊ C4×C5
HallC7×C13×C11⋊C5 ⋊ C4
HallDic1001 ⋊ C5
HallC13×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ Dic13
HallC11×C13 ⋊ C5×Dic7
HallC7×C13 ⋊ Dic11⋊C5
HallC7×C11 ⋊ C5×Dic13
HallC11⋊C5 ⋊ Dic91
SylowC13 ⋊ C7⋊(Dic11⋊C5)
SylowC11 ⋊ C5×Dic91
SylowC7 ⋊ (C11⋊C5)⋊Dic13

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C7⋊(C13⋊AGL(1,𝔽11))
commutator, hypocenterC7×C11×C13C4×C5
Fitting, socle, cosocleC2×C7×C11×C13C2×C5
prime radicalC2×C7×C13×C11⋊C5C2
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2

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)(26,27)(28,29)(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)(25,26,28,30,31,29,27)

Polycyclic presentation:

2,5,7,11,13,2|a^2=f,c^a=c^6,d^a=d^10,e^a=e^12,d^b=d^4

Conjugacy classes & character table

652 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 24);