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C7×#261×C11⋊C5 #34093451

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

Aliases

direct productC7×#261×C11⋊C5
unambiguous semidirect product(C11×#261)⋊(C5×C7)
unambiguous semidirect product(C7×C11×#261)⋊C5

Splittings

Fitting, socle, HallC7×C11×C13 ⋊ C4×C5
derived, HallC11×C13 ⋊ C4×C5×C7
HallC7×C13×C11⋊C5 ⋊ C4
HallC7×C11×#261 ⋊ C5
HallC13×C11⋊C5 ⋊ C4×C7
HallC11×#261 ⋊ C5×C7
HallC7×C13 ⋊ C4×C11⋊C5
HallC7×C11 ⋊ C5×#261
SylowC13 ⋊ C4×C7×C11⋊C5
SylowC11 ⋊ C5×C7×#261

Subgroups

subgroupG/H
center, hypercenterC7#261×C11⋊C5
commutator, hypocenterC11×C13C4×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C13C4×C5
prime radicalC7×D13×C11⋊C5C2
cosocleC11×D13C2×C5×C7
LCSG ▷ C11×C13
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 1001

A minimal faithful permutation representation — 2 generators on 31 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 28);