Finite Group Databasebeta

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Cayley diagram

C4×C22⋊D13 #88182

order416
isoclinismisoclinic class of Dic26
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D13

Splittings

FittingC22×C4×C13 ⋊ C2
SylowC13 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D13
commutatorC2×C13C22×C4
FrattiniC22C22×D13
FittingC22×C4×C13C2
socle, cosocleC22×C13C23
prime radicalC2×C22⋊D13C2
hypercenterC22×C4D13
hypocenterC13C4×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 208

A minimal faithful permutation representation — 3 generators on 21 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11718386, #11718389, #11718390, …
maximal normal subgroup of#11718386, #11718389, #11718390, …
maximal quotient ofC4×#6101, #11718594, C4×#6103, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 149);