Finite Group Databasebeta

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Cayley diagram

C4×C22⋊Dic7 #89981

order448
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×C22⋊Dic7

Splittings

SylowC7 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D7
commutatorC2×C7C2×C42
FrattiniC23C22×D7
FittingC23×C4×C7C2
socle, cosocleC23×C7C23
prime radicalC24×C7C22
hypercenterC23×C4D7
hypocenterC7C4×C22⋊C4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C23×C4

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 224

A minimal faithful permutation representation — 3 generators on 19 points:

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

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11725424, #11725434, #11725483, …
maximal normal subgroup of#11725424, #11725434, #11725483, …
maximal quotient ofC4×C22⋊(C7⋊C8), #11729283, C4×C7⋊#95, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 743);