Finite Group Databasebeta

← Prev (#34093502) Next (#34093504) →

C11×C7⋊#63118 #34093503

order20020
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C7⋊#63118
unambiguous semidirect productC7⋊(C11×#63118)

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C4
derived, HallC5×C7×C13 ⋊ C4×C11
HallC7×C11×C13 ⋊ Dic5
HallC5×C11×C13 ⋊ Dic7
HallC5×C7×C11 ⋊ #261
HallC11×C13 ⋊ Dic35
HallC7×C13 ⋊ C11×Dic5
HallC7×C11 ⋊ #63118
HallC5×C13 ⋊ C11×Dic7
HallC5×C11 ⋊ C7⋊#261
HallC5×C7 ⋊ C11×#261
SylowC13 ⋊ C11×Dic35
SylowC7 ⋊ C11×#63118
SylowC5 ⋊ C11×C7⋊#261

Subgroups

subgroupG/H
center, hypercenterC11C7⋊#63118
commutator, hypocenterC5×C7×C13C4×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C13C4
prime radicalC5×C7×C11×D13C2
cosocleC5×C7×D13C2×C11
LCSG ▷ C5×C7×C13
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 5005

A minimal faithful permutation representation — 2 generators on 36 points:

(2,6,4,3)(5,13,9,8)(7,10,12,11)(15,16)(17,18)(19,20)(22,23)(24,25)(26,27,28,29,30,31,32,33,34,35,36);(1,2,5,8,12,6,10,11,3,7,13,9,4)(14,15,17,19,20,18,16)(21,22,24,25,23)

Conjugacy classes & character table

1573 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20020, 80);