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Cayley diagram

C22×C37⋊C3 #89228

order444
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC22×C37⋊C3

Splittings

Fitting, socle, HallC22×C37 ⋊ C3
derived, SylowC37 ⋊ C22×C3

Subgroups

subgroupG/H
center, hypercenterC22C37⋊C3
commutator, cosocle, hypocenterC37C22×C3
FrattiniC1G
Fitting, socleC22×C37C3
LCSG ▷ C37
UCSC1 ◁ C22

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 41
transitive degreeμt(G) = 148

A minimal faithful permutation representation — 2 generators on 41 points:

(3,4)(6,7,9)(8,11,16)(10,14,13)(12,18,25)(15,20,22)(17,23,19)(21,28,32)(24,30,29)(26,33,27)(31,36,37)(34,38,35)(39,41,40);(1,2)(5,6,8,12,18,26,34,39,38,23,9,13,19,27,28,11,17,24,31,33,16,22,29,35,36,20,7,10,15,21,25,32,37,40,41,30,14)

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×Dic37⋊C3, (C22⋊D37)⋊C3, C2×C4×C37⋊C3, …
maximal normal subgroup ofC2×Dic37⋊C3, (C22⋊D37)⋊C3, C2×C4×C37⋊C3, …
maximal quotient ofC2×C4×C37⋊C3, D4×C37⋊C3, Q8×C37⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(444, 12);