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C7×(C11⋊C5)⋊#261 #34093449

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

Aliases

direct productC7×(C11⋊C5)⋊#261
unambiguous semidirect product(C11⋊C5)⋊(C7×#261)
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×C11⋊C5 ⋊ #261
HallC7×C13 ⋊ Dic11⋊C5
HallC7×C11 ⋊ C5×#261
HallC11⋊C5 ⋊ C7×#261
SylowC13 ⋊ C7×Dic11⋊C5
SylowC11 ⋊ C5×C7×#261

Subgroups

subgroupG/H
center, hypercenterC7(C11⋊C5)⋊#261
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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 26);