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C3×(C2×D7)⋊C8 #10620577

order672
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22

Aliases

direct productC3×(C2×D7)⋊C8

Splittings

FittingC2×C3×C7×C8 ⋊ C2
HallC3×C7 ⋊ C22⋊C8
SylowC7 ⋊ C3×C22⋊C8

Subgroups

subgroupG/H
centerC2×C3×C4C2×D7
commutatorC2×C7C2×C3×C8
FrattiniC2×C4C2×C3×D7
FittingC2×C3×C7×C8C2
socleC22×C3×C7C2×C4
prime radicalC22×C3×D7C4
cosocleC2×C4×C7C22×C3
hypercenterC2×C3×C8D7
hypocenterC7C3×C22⋊C8
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C8

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 336

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13052945, #13052946, #13052956, …
maximal normal subgroup of#13052945, #13052946, #13052956, …
maximal quotient ofC3×#89254, C3×#89251, C3×#89263, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(672, 159);