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Cayley diagram

C22×D47 #67345

order376
isoclinismisoclinic class of D47
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC22×D47
unambiguous semidirect productC47⋊C23
unambiguous semidirect product(C2×C47)⋊C22

Splittings

Fitting, socleC22×C47 ⋊ C2
derived, SylowC47 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC22D47
commutator, cosocle, hypocenterC47C23
FrattiniC1G
Fitting, socleC22×C47C2
LCSG ▷ C47
UCSC1 ◁ C22

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 51
transitive degreeμt(G) = 188

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D47)⋊C4, C2×C4×D47, C2×D188, …
maximal normal subgroup of(C2×D47)⋊C4, C2×C4×D47, C2×D188, …
maximal quotient ofC2×Dic94, C2×C4×D47, C2×D188, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(376, 11);