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Cayley diagram

C4×C7⋊D7 #87649

order392
isoclinismisoclinic class of C7⋊D7
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C7

Aliases

direct productC4×C7⋊D7

Splittings

FittingC4×C72 ⋊ C2
derived, SylowC72 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4C7⋊D7
commutator, hypocenterC72C2×C4
FrattiniC2C2×C7⋊D7
FittingC4×C72C2
socle, cosocleC2×C72C22
prime radicalC2×C7⋊D7C2
LCSG ▷ C72
UCSC1 ◁ C4

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 196

A minimal faithful permutation representation — 3 generators on 18 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716029, #11716031, C8×C7⋊D7, …
maximal normal subgroup of#11716029, #11716031, C8×C7⋊D7, …
maximal quotient ofC8×C7⋊D7, #11716061, C4×C7⋊Dic7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(392, 29);