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C11⋊C5×C7⋊#261 #34093458

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

Aliases

direct productC11⋊C5×C7⋊#261
unambiguous semidirect productC7⋊(#261×C11⋊C5)
unambiguous semidirect product(C11×C7⋊#261)⋊C5

Splittings

Fitting, socle, derived, HallC7×C11×C13 ⋊ C4×C5
HallC7×C13×C11⋊C5 ⋊ C4
HallC11×C7⋊#261 ⋊ C5
HallC13×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ #261
HallC11×C13 ⋊ C5×Dic7
HallC7×C13 ⋊ C4×C11⋊C5
HallC7×C11 ⋊ C5×#261
SylowC13 ⋊ Dic7×C11⋊C5
SylowC11 ⋊ C5×C7⋊#261
SylowC7 ⋊ #261×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC7×C11×C13C4×C5
prime radicalC7×D13×C11⋊C5C2
cosocleC7×C11×D13C2×C5
LCSG ▷ C7×C11×C13
UCSC1

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:

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

Conjugacy classes & character table

217 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 35);