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C2×#23751215 #34063595

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

Aliases

direct productC2×#23751215

Splittings

Fitting, socleC2×C312 ⋊ C2×C5
derived, SylowC312 ⋊ C22×C5
Hall#18012457 ⋊ C22
HallC2×C31⋊D31 ⋊ C5

Subgroups

subgroupG/H
center, hypercenterC2#23751215
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)(33,37,36,45,46,34,35,39,40,55)(38,52,53,54,56,43,44,60,61,59)(41,49,50,57,58,48,42,51,47,62);(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)(32,33,36,41,46,56,50,49,35,38,44,54,58,60,57,45,40,47,53,62,61,52,43,37,42,51,59,55,48,39,34)(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, 52);