Finite Group Databasebeta

← Prev (#34063591) Next (#34063593) →

C2×#23751212 #34063592

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

Aliases

direct productC2×#23751212

Splittings

Fitting, socleC2×C312 ⋊ C2×C5
derived, SylowC312 ⋊ C22×C5
Hall#18012456 ⋊ C22
HallC2×C31⋊D31 ⋊ C5

Subgroups

subgroupG/H
center, hypercenterC2#23751212
commutator, cosocle, hypocenterC312C22×C5
FrattiniC1G
Fitting, socleC2×C312C2×C5
LCSG ▷ C312
UCSC1 ◁ C2

340 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 64
transitive degreeμt(G) = 1922

A minimal faithful permutation representation — 3 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)(33,37,38,49,36,34,35,42,43,40)(39,54,55,56,41,45,46,58,60,48)(44,61,53,59,47,51,52,62,50,57);(32,33,36,41,43,50,60,54,38,44,53,61,55,57,45,37,35,39,47,58,52,62,51,42,46,56,59,49,48,40,34)(63,64);(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)

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, 49);