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C7×Dic13×C11⋊C5 #34093441

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C7D13×C11⋊C5
commutator, hypocenterC11×C13C4×C5×C7
FrattiniC2C7×D13×C11⋊C5
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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 18);