Finite Group Databasebeta

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Cayley diagram

D7×C4⋊C8 #89604

order448
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD7×C4⋊C8

Splittings

FittingC7×C4⋊C8 ⋊ C2
SylowC7 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D7
commutatorC2×C7C22×C8
FittingC7×C4⋊C8C2
socleC22×C7C22×C4
prime radicalC22×D7C2×C4
cosocleC2×C4×C7C23
hypercenterC4⋊C8D7
hypocenterC7C2×C4⋊C8
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C4⋊C8

138 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:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×D4⋊C8, #11725920, #11725922, …
maximal normal subgroup ofD7×D4⋊C8, #11725920, #11725922, …
maximal quotient ofD7×#334, #11726281, #11726282, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 366);