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C7×C19×#1042 #27210902

order13300
isoclinismisoclinic class of #1042
automorphism?
homologyAbelianization (H1) = C4×C7×C19 · Schur multiplier (H2) = C1

Aliases

direct productC7×C19×#1042

Splittings

Fitting, socle, HallC52×C7×C19 ⋊ C4
derived, SylowC52 ⋊ C4×C7×C19
HallC52×C19 ⋊ C4×C7
HallC52×C7 ⋊ C4×C19

Subgroups

subgroupG/H
center, hypercenterC7×C19#1042
commutator, hypocenterC52C4×C7×C19
FrattiniC1G
Fitting, socleC52×C7×C19C4
prime radicalC5×C7×D5×C19C2
cosocleC5×D5C2×C7×C19
LCSG ▷ C52
UCSC1 ◁ C7×C19

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 2660

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

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

Conjugacy classes & character table

1729 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13300, 60);