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Cayley diagram

C22×D49 #87632

order392
isoclinismisoclinic class of D49
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC22×D49
unambiguous semidirect productC49⋊C23
unambiguous semidirect product(C2×C49)⋊C22

Splittings

FittingC22×C49 ⋊ C2
derived, SylowC49 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC22D49
commutator, cosocle, hypocenterC49C23
FrattiniC7C22×D7
FittingC22×C49C2
socleC22×C7D7
LCSG ▷ C49
UCSC1 ◁ C22

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 196

A minimal faithful permutation representation — 3 generators on 53 points:

(1,2)(3,4)(6,8)(7,11)(9,14)(10,17)(12,20)(13,19)(15,24)(16,27)(18,29)(21,33)(22,32)(23,31)(25,36)(26,38)(28,40)(30,42)(34,43)(35,44)(37,46)(39,48)(41,50)(45,51)(47,52)(49,53);(3,4)(5,10,28,49,48,27,8,7,18,41,52,38,14,13,12,30,51,46,24,23,22,21,43,44,36,25,35,34,33,32,31,15,37,45,42,20,19,9,26,47,50,29,11,6,16,39,53,40,17);(1,2)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D49)⋊C4, C2×C4×D49, C2×D196, …
maximal normal subgroup of(C2×D49)⋊C4, C2×C4×D49, C2×D196, …
maximal quotient ofC2×Dic98, C2×C4×D49, C2×D196, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 12);