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C37×#329 #14556994

order2368
nilpotency class3
isoclinismisoclinic class of #327
automorphism?
homologyAbelianization (H1) = C2×C4×C37 · Schur multiplier (H2) = C2

Aliases

direct productC37×#329

Subgroups

subgroupG/H
center, socleC22×C37C22⋊C4
commutatorC2×C4C2×C4×C37
Frattini, cosocleC42C22×C37
prime radicalC2×D4×C37C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C42×C37 ◁ G

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 1184

A minimal faithful permutation representation — 2 generators on 53 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)(47,50,51,52);(39,42)(40,44)(46,47)(48,52)(49,51)(50,53)

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37×#1403, C37×#1404, C2×C37×#329, …
maximal normal subgroup ofC37×#1403, C37×#1404, C2×C37×#329, …
maximal quotient ofC37×#1270, C37×#1272, C37×#1295, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 10);