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C19×C7⋊#1043 #27210896

order13300
automorphism?
homologyAbelianization (H1) = C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C7⋊#1043
unambiguous semidirect productC7⋊(C19×#1043)

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C4
derived, HallC52×C7 ⋊ C4×C19
HallC52×C19 ⋊ Dic7
HallC7×C19 ⋊ #1043
SylowC52 ⋊ C19×Dic7
SylowC7 ⋊ C19×#1043

Subgroups

subgroupG/H
center, hypercenterC19C7⋊#1043
commutator, hypocenterC52×C7C4×C19
FrattiniC1G
Fitting, socleC52×C7×C19C4
prime radicalC7×C19×C5⋊D5C2
cosocleC7×C5⋊D5C2×C19
LCSG ▷ C52×C7
UCSC1 ◁ C19

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 3325

A minimal faithful permutation representation — 3 generators on 36 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 54);