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Cayley diagram

C2×Dic37 #64442

order296
isoclinismisoclinic class of D37
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productC2×Dic37

Splittings

derived, SylowC37 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22D37
commutator, hypocenterC37C2×C4
FrattiniC2C2×D37
Fitting, socle, prime radicalC22×C37C2
cosocleC2×C37C22
LCSG ▷ C37
UCSC1 ◁ C22

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 296

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×Dic37, #10596936, C4⋊Dic37, …
maximal normal subgroup ofC4×Dic37, #10596936, C4⋊Dic37, …
maximal quotient ofC2×#64436, #10596934, C4×Dic37, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(296, 7);