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Cayley diagram

C2×Dic38 #64538

order304
isoclinismisoclinic class of Dic38
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic38
unambiguous semidirect product(C2×C19)⋊Q8

Splittings

SylowC19 ⋊ C2×Q8

Subgroups

subgroupG/H
centerC22C2×D19
commutator, cosocleC2×C19C23
FrattiniC2C22×D19
FittingC2×C4×C19C2
socle, prime radicalC22×C19C22
hypercenterC2×C4D19
hypocenterC19C2×Q8
LCSG ▷ C2×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C4

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 304

A minimal faithful permutation representation — 3 generators on 29 points:

(3,5,6,10)(4,7,8,9)(11,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13);(1,2)(3,4,6,8)(5,9,10,7)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29);(1,2)

Conjugacy classes & character table

82 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10597267, #10597273, #10597281, …
maximal normal subgroup of#10597267, #10597273, #10597281, …
maximal quotient ofC4×Dic38, #10597315, #10597316, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(304, 27);