Finite Group Databasebeta

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Cayley diagram

C2×C22⋊Dic13 #88206

order416
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊Dic13

Splittings

SylowC13 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D13
commutatorC2×C13C22×C4
FrattiniC22C22×D13
Fitting, prime radicalC24×C13C2
socleC23×C13C22
cosocleC22×C13C23
hypercenterC24D13
hypocenterC13C2×C22⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 208

A minimal faithful permutation representation — 3 generators on 23 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11718118, #11718119, #11718305, …
maximal normal subgroup of#11718118, #11718119, #11718305, …
maximal quotient ofC2×C22⋊#1055, #11718868, C2×#88071, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 173);