Finite Group Databasebeta

← Prev (#17990375) Next (#17990377) →

C37×#1558 #17990376

order4736
nilpotency class3
isoclinismisoclinic class of #1510
automorphism?
homologyAbelianization (H1) = C22×C4×C37 · Schur multiplier (H2) = C23

Aliases

direct productC37×#1558

Subgroups

subgroupG/H
center, socleC22×C37C2×C22⋊C4
commutatorC2×C4C22×C4×C37
Frattini, cosocleC42C23×C37
prime radicalC23×C37C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 61
transitive degreeμt(G) = 2368

A minimal faithful permutation representation — 3 generators on 61 points:

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

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#7483, C37×#8498, C37×#8524, …
maximal normal subgroup ofC37×#7483, C37×#8498, C37×#8524, …
maximal quotient ofC37×#7595, C37×#7605, C37×#7629, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 290);