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C2×#23751218 #34063598

order19220
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C31

Aliases

direct productC2×#23751218

Splittings

Fitting, socleC2×C312 ⋊ C2×C5
derived, SylowC312 ⋊ C22×C5
Hall#18012458 ⋊ C22
HallC2×C31⋊D31 ⋊ C5

Subgroups

subgroupG/H
center, hypercenterC2#23751218
commutator, cosocle, hypocenterC312C22×C5
FrattiniC1G
Fitting, socleC2×C312C2×C5
LCSG ▷ C312
UCSC1 ◁ C2

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 64
transitive degreeμt(G) = 310

A minimal faithful permutation representation — 2 generators on 64 points:

(2,6,7,18,5,3,4,11,12,9)(8,23,24,25,10,14,15,27,29,17)(13,30,22,28,16,20,21,31,19,26)(33,36,37,44,45,34,35,39,40,52)(38,49,50,51,54,42,43,60,53,62)(41,57,58,55,56,47,48,59,46,61);(1,2,5,10,12,19,29,23,7,13,22,30,24,26,14,6,4,8,16,27,21,31,20,11,15,25,28,18,17,9,3)(32,33,35,38,37,41,43,51,40,46,48,59,50,61,62,52,45,54,56,60,58,57,55,44,53,49,47,39,42,36,34)(63,64)

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19220, 55);