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Q82×C37 #14557223

order2368
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C37 · Schur multiplier (H2) = C24

Aliases

direct productQ82×C37

Subgroups

subgroupG/H
center, socle, prime radicalC22×C37C24
commutator, Frattini, cosocleC22C24×C37
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 2368

A minimal faithful permutation representation — 4 generators on 53 points:

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

Conjugacy classes & character table

925 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#1623, C37×#1633, C37×#1645, …
maximal normal subgroup ofC37×#1623, C37×#1633, C37×#1645, …
maximal quotient ofQ8×C4⋊C4×C37, C37×#2369, C37×#2451, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 239);